# Quiz 11: Introduction to Hypothesis Testing

Statistics

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Q 2Q 2

An alternative or research hypothesis is an assertion that holds if the null hypothesis is false.

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Q 3Q 3

A Type I error is represented by ; it is the probability of rejecting a true null hypothesis.

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Q 6Q 6

Increasing the probability of a Type I error will increase the probability of a Type II error.

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A Type II error is represented by ; it is the probability of rejecting a true null hypothesis.

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Q 12Q 12

A Type II error is represented by ; it is the probability of failing to reject a false null hypothesis.

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Q 13Q 13

In testing a hypothesis, statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data.

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Q 15Q 15

There is an inverse relationship between the probabilities of Type I and Type II errors; as one increases, the other decreases, and vice versa.

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Q 16Q 16

A professor of linguistics refutes the claim that the average student spends 3 hours studying for the midterm exam.She thinks they spend more time than that.Which hypotheses are used to test the claim?
A) H

_{0}: 3 vs.H_{1}: 3 B) H_{0}: 3 vs.H_{1}: 3 C) H_{0}: 3 vs.H_{1}: 3 D) H_{0}: 3 vs.H_{1}: 3Free

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Q 18Q 18

A Type I error is committed if we make:
A) a correct decision when the null hypothesis is false.
B) a correct decision when the null hypothesis is true.
C) an incorrect decision when the null hypothesis is false.
D) an incorrect decision when the null hypothesis is true.

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Q 19Q 19

A Type II error is committed if we make:
A) a correct decision when the null hypothesis is false.
B) a correct decision when the null hypothesis is true.
C) an incorrect decision when the null hypothesis is false.
D) an incorrect decision when the null hypothesis is true.

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Q 20Q 20

The hypothesis of most interest to the researcher is:
A) the alternative hypothesis.
B) the null hypothesis.
C) both hypotheses are of equal interest.
D) Neither hypothesis is of interest.

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Q 21Q 21

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200.The correct set of hypotheses is:
A) H

_{0}: 1200 vs.H_{1}: 1200 B) H_{0}: 1200 vs.H_{1}: 1200 C) H_{0}: 1200 vs.H_{1}: 1200 D) H_{0}: 1200 vs.H_{1}: 1200Free

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Q 22Q 22

Which of the following conclusions is not an appropriate conclusion from a hypothesis test?
A) Reject H

_{0}.Sufficient evidence to support H_{1}. B) Fail to reject H_{0}.Insufficient evidence to support H_{1}. C) Accept H_{0}.Sufficient evidence to support H_{0}. D) All of these choices are true.Free

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Q 23Q 23

A Type I error occurs when we:
A) reject a false null hypothesis.
B) reject a true null hypothesis.
C) don't reject a false null hypothesis.
D) don't reject a true null hypothesis.

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Q 24Q 24

A Type II error is defined as:
A) rejecting a true null hypothesis.
B) rejecting a false null hypothesis.
C) not rejecting a true null hypothesis.
D) not rejecting a false null hypothesis.

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Q 26Q 26

In a criminal trial, a Type I error is made when:
A) a guilty defendant is acquitted.
B) an innocent person is convicted.
C) a guilty defendant is convicted.
D) an innocent person is acquitted.

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Q 27Q 27

In a criminal trial, a Type II error is made when:
A) a guilty defendant is acquitted.
B) an innocent person is convicted.
C) a guilty defendant is convicted.
D) an innocent person is acquitted.

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Q 28Q 28

We cannot commit a Type I error when the:
A) null hypothesis is true.
B) level of significance is 0.10.
C) null hypothesis is false.
D) test is a two-tail test.

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Q 29Q 29

The level of significance can be:
A) any number between 1.0 and 1.0.
B) any number greater than zero.
C) any number greater than 1.96 or less than 1.96.
D) None of these choices.

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Q 30Q 30

Which of the following is an appropriate null hypothesis?
A) The mean of a population is equal to 60.
B) The mean of a sample is equal to 60.
C) The mean of a population is not equal to 60.
D) All of these choices are true.

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Q 31Q 31

Which of the following statements is not true?
A) The probability of making a Type II error increases as the probability of making a Type I error decreases.
B) The probability of making a Type II error and the level of significance are the same.
C) The power of the test decreases as the level of significance decreases.
D) All of these choices are true.

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Q 32Q 32

Which of the following would be an appropriate alternative hypothesis?
A) The mean of a population is equal to 70.
B) The mean of a sample is equal to 70.
C) The mean of a population is greater than 70.
D) The mean of a sample is greater than 70.

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Q 33Q 33

If a test of hypothesis has a Type I error probability of .05, this means that:
A) if the null hypothesis is true, we don't reject if 5% of the time.
B) if the null hypothesis is true, we reject it 5% of the time.
C) if the null hypothesis is false, we don't reject it 5% of the time.
D) if the null hypothesis is false, we reject it 5% of the time.

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Q 34Q 34

Suppose we wish to test H

_{0}: vs.H_{1}: 45.What will result if we conclude that the mean is greater than 45 when the actual mean is 50? A) We have made a Type I error. B) We have made a Type II error. C) We have made both a Type I error and a Type II error. D) We have made the correct decision.Free

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Q 35Q 35

Which of the following probabilities is equal to the significance level ?
A) Probability of making a Type I error.
B) Probability of making a Type II error.
C) Probability of rejecting H

_{0}when you are supposed to. D) Probability of not rejecting H_{0}when you shouldn't.Free

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Q 36Q 36

If we reject the null hypothesis when it is false, then we have committed:
A) a Type II error.
B) a Type I error.
C) both a Type I error and a Type II error.
D) neither a Type I error nor a Type II error.

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Q 37Q 37

Researchers claim that 40 tissues is the average number of tissues a person uses during the course of a cold.The company who makes Puffs brand tissues thinks that fewer of their tissues are needed.What are their null and alternative hypotheses?
A) H

_{0}: 40 vs.H_{1}: 40 B) H_{0}: 40 vs.H_{1}: 40 C) H_{0}: 40 vs.H_{1}: 40 D) H_{0}: 40 vs.H_{1}: 40Free

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Q 38Q 38

The owner of a local Jazz Club has recently surveyed a random sample of n = 200 customers of the club.She would now like to determine whether or not the mean age of her customers is over 30.If so, she plans to alter the entertainment to appeal to an older crowd.If not, no entertainment changes will be made.The appropriate hypotheses to test are:
A) H

_{0}: 30 vs.H_{1}: 30. B) H_{0}: 30 vs.H_{1}: 30. C) H_{0}: 30 vs.H_{1}: 30. D) H_{0}: 30 vs.H_{1}: 30.Free

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Q 39Q 39

If a researcher rejects a true null hypothesis, she has made a(n) ____________________ error.

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Q 40Q 40

If a researcher fails to reject a false null hypothesis he has made a(n) ____________________ error.

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Q 41Q 41

If a researcher rejects a false null hypothesis, she has made a(n) ____________________ decision.

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Q 42Q 42

If a researcher fails to reject a true null hypothesis, he has made a(n) ____________________ decision.

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Q 47Q 47

The hypothesis testing procedure begins with the assumption that the null hypothesis is ____________________.

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Q 48Q 48

After you set up the hypotheses and collect your data, you calculate the statistic that serves as the criterion for making your decision.This number is called the ____________________ statistic.

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Q 49Q 49

Suppose an auto manufacturer states that their car goes from 0 to 60 miles per hour in 10 seconds on average, and you suspect that time is longer.
a.
Set up the null and alternative hypotheses to test this claim.
b.
Explain how you know which is the null hypothesis and which is the alternative hypothesis.

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Q 50Q 50

Suppose a pickup and delivery company states that their packages arrive within two days or less on average.You want to find out whether the actual average delivery time is longer than this.You conduct a hypothesis test.
a.
Set up the null and alternative hypotheses.
b.
Suppose you conclude wrongly that the company's statement about average delivery time is within two days.What type of error is being committed and what is the impact of that error?
c.
Suppose you conclude wrongly that the delivery company's average time to delivery is in fact longer than two days.What type of error did you commit and what is the impact of this error?
d.
Which error is worse from the company's standpoint, a Type I or a Type II error? Why?
e.
Which error is worse from a consumer standpoint, a Type I or a Type II error? Why?

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Q 53Q 53

Think about a situation where you have a test for a virus.First, you are tested positive or negative.Second, you either really do have the virus or you don't.
a.
If you actually have the virus but the test did not catch it, which error has been made and what is the impact of that error?
b.
If you actually don't have the virus but the test says you did, which error is being made and what is the impact of this error?
c.
Which error is the worst one to commit in this situation and why?

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Q 54Q 54

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true.

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Q 60Q 60

In a one-tail test, the p-value is found to be equal to 0.054.If the test had been two-tail, then the p-value would have been 0.027.

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Q 61Q 61

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will decrease.

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Q 62Q 62

The critical values will bound the rejection and non-rejection regions for the null hypothesis.

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Q 63Q 63

If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the null hypothesis is true.

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Q 64Q 64

If a null hypothesis is rejected at the 0.05 level of significance, it must be rejected at the 0.025 level.

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Q 65Q 65

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 78.21 to 87.64.If the same sample had been used to test the null hypothesis that the mean of the population differs from 90, the null hypothesis could be rejected at a level of significance of 0.05.

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Q 66Q 66

If we reject a null hypothesis at the 0.05 level of significance, then we must also reject it at the 0.10 level.

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Q 69Q 69

A one-tail test for the population mean produces a test-statistic z = 0.75.The p-value associated with the test is 0.7734.

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Q 70Q 70

Using the confidence interval when conducting a two-tail test for the population mean , we do not reject the null hypothesis if the hypothesized value for falls between the lower and upper confidence limits.

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Q 71Q 71

A two-tail test for the population mean produces a test-statistic z = 1.89.The p-value associated with the test is 0.0588.

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Q 72Q 72

For a given level of significance, if the sample size is increased, the probability of committing a Type I error will decrease.

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Q 73Q 73

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 10.89 to 13.21.If the same sample had been used to test H

_{0}: = 12 vs.H_{1}: 12, H_{0}could not be rejected at the 0.05 level.Free

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Q 74Q 74

If we reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

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Q 76Q 76

In order to determine the p-value, which of the following is not needed?
A) The level of significance.
B) Whether the test is one-tail or two-tail.
C) The value of the test statistic.
D) All of these choices are true.

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Q 77Q 77

Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.05?
A) 0.150
B) 0.100
C) 0.051
D) 0.025

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Q 78Q 78

If a hypothesis is not rejected at the 0.10 level of significance, it:
A) must be rejected at the 0.05 level.
B) may be rejected at the 0.05 level.
C) will not be rejected at the 0.05 level.
D) must be rejected at the 0.025 level.

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Q 79Q 79

In testing the hypotheses H

_{0}: 75 vs.H_{1}: < 75, if the value of the test statistic z equals 2.42, then the p-value is: A) 0.5078 B) 2.4200 C) 0.9922 D) 0.0078Free

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Q 80Q 80

For a two-tail test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardized test statistic z is:
A) smaller than 1.96 or greater than 1.96
B) greater than 1.96 or smaller than 1.96
C) smaller than 1.96 or greater than 1.96
D) greater than 1.645 or less than 1.645

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Q 81Q 81

In testing the hypotheses H

_{0}: 800 vs.H_{1}: 800, if the value of the test statistic equals 1.75, then the p-value is: A) 0.0401 B) 0.0802 C) 0.4599 D) 0.9599Free

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Q 82Q 82

If a hypothesis is rejected at the 0.025 level of significance, it:
A) must be rejected at any level.
B) must be rejected at the 0.01 level.
C) must not be rejected at the 0.01 level.
D) may or may not be rejected at the 0.01 level.

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Q 83Q 83

Suppose that we reject a null hypothesis at the 0.05 level of significance.Then for which of the following -values do we also reject the null hypothesis?
A) 0.06
B) 0.04
C) 0.03
D) 0.02

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Q 84Q 84

The critical values z

_{}or z_{}_{ / 2}are the boundary values for: A) the rejection region(s). B) the level of significance. C) Type I error. D) Type II error.Free

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Q 85Q 85

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true:
A) a Type I error is committed.
B) a Type II error is committed.
C) a correct decision is made.
D) a one-tail test should be used instead of a two-tail test.

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Q 86Q 86

Using a confidence interval when conducting a two-tail test for , we do not reject H

_{0}if the hypothesized value for : A) is to the left of the lower confidence limit (LCL). B) is to the right of the upper confidence limit (UCL). C) falls between the LCL and UCL. D) falls in the rejection region.Free

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Q 87Q 87

In a two-tail test for the population mean, the null hypothesis will be rejected at level of significance if the value of the standardized test statistic z is such that:
A) z > z

_{}B) z < z_{}C) z_{}< z < z_{}D) | z | > z_{}_{ }_{/ 2}Free

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Q 88Q 88

In testing the hypothesis H

_{0}: 100 vs.H_{1}: > 100, the p-value is found to be 0.074, and the sample mean is 105.Which of the following statements is true? A) The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is 0.074. B) The probability of observing a sample mean smaller than 105 from a population whose mean is 100 is 0.074. C) The probability that the population mean is larger than 100 is 0.074. D) None of these choices.Free

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Q 89Q 89

If we reject the null hypothesis, we conclude that:
A) there is enough statistical evidence to infer that the alternative hypothesis is true.
B) there is not enough statistical evidence to infer that the alternative hypothesis is true.
C) there is enough statistical evidence to infer that the null hypothesis is true.
D) there is not enough statistical evidence to infer that the null hypothesis is true.

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Q 90Q 90

Suppose that in a certain hypothesis test the null hypothesis is rejected at the .10 level; it is also rejected at the .05 level; however it cannot be rejected at the .01 level.The most accurate statement that can be made about the p-value for this test is that:
A) p-value = 0.01.
B) p-value = 0.10.
C) 0.01 < p-value < 0.05.
D) 0.05 < p-value < 0.10.

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Q 91Q 91

Statisticians can translate p-values into several descriptive terms.Suppose you typically reject H

_{0}at level 0.05.Which of the following statements is correct? A) If the p-value < 0.001, there is overwhelming evidence to infer that the alternative hypothesis is true. B) If 0.01 < p-value < 0.05, there is evidence to infer that the alternative hypothesis is true. C) If p-value > 0.10, there is no evidence to infer that the alternative hypothesis is true. D) All of these choices are true.Free

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Q 92Q 92

If we do not reject the null hypothesis, we conclude that:
A) there is enough statistical evidence to infer that the alternative hypothesis is true.
B) there is not enough statistical evidence to infer that the alternative hypothesis is true.
C) there is enough statistical evidence to infer that the null hypothesis is true.
D) there is not enough statistical evidence to infer that the null hypothesis is true.

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Q 93Q 93

In a one-tail test, the p-value is found to be equal to 0.068.If the test had been two-tail, the p-value would have been:
A) 0.932
B) 0.466
C) 0.034
D) 0.136

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Q 94Q 94

The p-value of a test is the:
A) smallest at which the null hypothesis can be rejected.
B) largest at which the null hypothesis can be rejected.
C) smallest at which the null hypothesis cannot be rejected.
D) largest at which the null hypothesis cannot be rejected.

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Q 95Q 95

We have created a 95% confidence interval for with the result (8, 13).What conclusion will we make if we test H

_{0}: 15 vs.H_{1}: 15 at = 0.05? A) Reject H_{0}in favor of H_{1}B) Accept H_{0}in favor of H_{1}C) Fail to reject H_{0}in favor of H_{1}D) We cannot tell what our decision will be from the information givenFree

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Q 96Q 96

The p-value criterion for hypothesis testing is to reject the null hypothesis if:
A) p-value =
B) p-value <
C) p-value >
D) < p-value <

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Q 97Q 97

If the p value is less than in a two-tail test:
A) the null hypothesis should not be rejected.
B) the null hypothesis should be rejected.
C) a one-tail test should be used.
D) No conclusion should be reached.

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Q 98Q 98

If a marketer wishes to determine whether there is evidence that average family income in a community exceeds $32,000:
A) either a one-tail or two-tail test could be used with equivalent results.
B) a one-tail test should be utilized.
C) a two-tail test should be utilized.
D) None of these choices.

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Q 99Q 99

We have created a 95% confidence interval for with the results (10, 25).What conclusion will we make if we test H

_{0}: 26 vs.H_{1}: 26 at = 0.025? A) Reject H_{0}in favor of H_{1}B) Accept H_{0}in favor of H_{1}C) Fail to reject H_{0}in favor of H_{1}D) We cannot tell from the information given.Free

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Q 100Q 100

The rejection region for testing H

_{0}: 100 vs.H_{1}: 100, at the 0.05 level of significance is: A) | z | < 0.95 B) | z | > 1.96 C) z > 1.65 D) z < 2.33Free

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Q 101Q 101

The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club.She would now like to determine whether or not the mean age of her customers is over 35.If so, she plans to alter the entertainment to appeal to an older crowd.If not, no entertainment changes will be made.Suppose she found that the sample mean was 35.5 years and the population standard deviation was 5 years.What is the p-value associated with the test statistic?
A) 0.9582
B) 1.7300
C) 0.0418
D) 0.0836

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Q 102Q 102

The rejection region for testing H

_{0}: 80 vs.H_{1}: 80, at the 0.10 level of significance is: A) z > 1.96 B) z < 0.90 C) z > 1.28 D) z < 1.28Free

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Q 103Q 103

We have created a 90% confidence interval for with the result (25, 32).What conclusion will we make if we test H

_{0}: 28 vs.H_{1}: 28 at = 0.10? A) Reject H_{0}in favor of H_{1}. B) Accept H_{0}in favor of H_{1}. C) Fail to reject H_{0}in favor of H_{1}. D) We cannot tell from the information given.Free

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Q 104Q 104

The numerical quantity computed from the data that is used in deciding whether to reject H

_{0}is the: A) significance level. B) critical value. C) test statistic. D) parameter.Free

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Q 105Q 105

The owner of a local Karaoke Bar has recently surveyed a random sample of n = 300 customers of the bar.She would now like to determine whether or not the mean age of her customers is over 35.If so, she plans to alter the entertainment to appeal to an older crowd.If not, no entertainment changes will be made.If she wants to be 99% confident in her decision, what rejection region she use if the population standard deviation is known?
A) Reject H

_{0}if z < 2.33 B) Reject H_{0}if z < 2.58 C) Reject H_{0}if z > 2.33 D) Reject H_{0}if z > 2.58Free

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Q 106Q 106

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the ____________________ method.The other approach is the p-value method.

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Q 107Q 107

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the rejection region method.The other approach is the ____________________ method.

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Q 108Q 108

The ____________________ is a range of values such that if the test statistic falls into that range we reject the null hypothesis in favor of the alternative
hypothesis.

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Q 109Q 109

The probability of a test statistic falling in the rejection region is equal to the value of ____________________.

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Q 110Q 110

When a null hypothesis is rejected, the test is said to be statistically ____________________ at level .

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Q 111Q 111

If the conclusion of a hypothesis test is that a statistically significant result was found, then the null hypothesis ____________________ (was/was not) rejected.

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Q 112Q 112

The ____________________ of a test is the probability of observing a test statistic at least as extreme as the one from your sample, given that H

_{0}is true.Free

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Q 113Q 113

You reject H

_{0}if the p-value of your hypothesis is ____________________ than the significance level.Free

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Q 114Q 114

The ____________________ is a measure of the amount of statistical evidence that supports the alternative hypothesis.

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Q 115Q 115

If we do not reject the null hypothesis, we conclude that there ____________________(is/is not) enough statistical evidence to infer that the alternative hypothesis is true.

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Q 116Q 116

Production Filling
A production filling operation has a historical standard deviation of 6 ounces.When in proper adjustment, the mean filling weight for the production process is 50 ounces.A quality control inspector periodically selects at random 36 containers and uses the sample mean filling weight to see if the process is in proper adjustment.
-{Production Filling Narrative} State the null and alternative hypotheses.

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Q 117Q 117

Production Filling
A production filling operation has a historical standard deviation of 6 ounces.When in proper adjustment, the mean filling weight for the production process is 50 ounces.A quality control inspector periodically selects at random 36 containers and uses the sample mean filling weight to see if the process is in proper adjustment.
-{Production Filling Narrative} Using a standardized test statistic, test the hypothesis at the 5% level of significance if the sample mean filling weight is 48.6 ounces.

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Q 118Q 118

Production Filling
A production filling operation has a historical standard deviation of 6 ounces.When in proper adjustment, the mean filling weight for the production process is 50 ounces.A quality control inspector periodically selects at random 36 containers and uses the sample mean filling weight to see if the process is in proper adjustment.
-{Production Filling Narrative} Develop a 95% confidence interval and use it to test the hypothesis.

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Q 119Q 119

A social researcher claims that the average adult listens to the radio less than 26 hours per week.He collects data on 25 individuals' radio listening habits and finds that the mean number of hours that the 25 people spent listening to the radio was 22.4 hours.If the population standard deviation is known to be eight hours, can we conclude at the 1% significance level that he is right?

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Q 120Q 120

A random sample of 100 observations from a normal population whose standard deviation is 50 produced a mean of 75.Does this statistic provide sufficient evidence at the 5% level of significance to infer that the population mean is not 80?

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Q 121Q 121

In testing the hypotheses H

_{0}: 50 vs.H_{1}: < 50, we found that the standardized test statistic is z = 1.59.Calculate the p-value, and state your conclusion if = .025.Free

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Q 122Q 122

Suppose that 10 observations are drawn from a normal population whose variance is 64.The observations are: 58, 62, 45, 50, 59, 65, 39, 40, 41, and 52.Test at the 10% level of significance to determine if there is enough evidence to conclude that the population mean is greater than 45.

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Q 123Q 123

Suppose that 9 observations are drawn from a normal population whose standard deviation is 2.The observations are: 15, 9, 13, 11, 8, 12, 11, 7, and 10.At 95% confidence, you want to determine whether the mean of the population from which this sample was taken is significantly different from 10.
a.
State the null and alternative hypotheses.
b.
Compute the value of the test statistic.
c.
Compute the p-value.
d.
Interpret the results.

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Q 124Q 124

Determine the p-value associated with each of the following values of the standardized test statistic z, and state your conclusion.
a.
two-tail test, with z = 1.50, and = .10
b.
one-tail test, with z = 1.05, and = .05
c.
one-tail test, with z = 2.40, and = .01

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Q 125Q 125

Watching the News
A researcher claims viewers spend an average of 40 minutes per day watching the news.You think the average is higher than that.In testing your hypotheses H

_{0}: 40 vs.H_{1}: > 40, the following information came from your random sample of viewers: = 42 minutes, n = 25.Assume = 5.5, and = 0.10. -{Watching the News Narrative} Calculate the value of the test statistic.Free

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Q 126Q 126

Watching the News
A researcher claims viewers spend an average of 40 minutes per day watching the news.You think the average is higher than that.In testing your hypotheses H

_{0}: 40 vs.H_{1}: > 40, the following information came from your random sample of viewers: = 42 minutes, n = 25.Assume = 5.5, and = 0.10. -{Watching the News Narrative} Set up the rejection region.Free

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Q 127Q 127

Watching the News
A researcher claims viewers spend an average of 40 minutes per day watching the news.You think the average is higher than that.In testing your hypotheses H

_{0}: 40 vs.H_{1}: > 40, the following information came from your random sample of viewers: = 42 minutes, n = 25.Assume = 5.5, and = 0.10. -{Watching the News Narrative} Determine the p-value.Free

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Q 128Q 128

Watching the News
A researcher claims viewers spend an average of 40 minutes per day watching the news.You think the average is higher than that.In testing your hypotheses H

_{0}: 40 vs.H_{1}: > 40, the following information came from your random sample of viewers: = 42 minutes, n = 25.Assume = 5.5, and = 0.10. -{Watching the News Narrative} Interpret the result.Free

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Q 129Q 129

LSAT Scores
The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for LSAT scores is 125.A random sample of 25 scores had an average of 1,375.
-{LSAT Scores Narrative} State the appropriate null and alternative hypotheses.

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Q 130Q 130

LSAT Scores
The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for LSAT scores is 125.A random sample of 25 scores had an average of 1,375.
-{LSAT Scores Narrative} Calculate the value of the test statistic and set up the rejection region at the 0.025 level.What is your conclusion?

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Q 131Q 131

LSAT Scores
The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for LSAT scores is 125.A random sample of 25 scores had an average of 1,375.
-{LSAT Scores Narrative} Calculate the p-value.

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Q 132Q 132

LSAT Scores
The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for LSAT scores is 125.A random sample of 25 scores had an average of 1,375.
-{LSAT Scores Narrative} Use the p-value to test the hypotheses.

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Q 133Q 133

LSAT Scores
The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for LSAT scores is 125.A random sample of 25 scores had an average of 1,375.
-With the following p-values, would you reject or fail to reject the null hypothesis? Comment on the statistical significance of each result.(Assume you normally reject H

_{0}at level 0.08.) a. p-value = 0.0025 b. p-value = 0.0328 c. p-value = 0.0795 d. p-value = 0.1940Free

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Q 134Q 134

Marathon Runners
A researcher wants to study the average miles run per day for marathon runners.In testing the hypotheses: H

_{0}: 25 miles vs.H_{1}: 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. -{Marathon Runners Narrative} Compute the value of the test statistic and specify the rejection region associated with 5% significance level.Free

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Q 135Q 135

Marathon Runners
A researcher wants to study the average miles run per day for marathon runners.In testing the hypotheses: H

_{0}: 25 miles vs.H_{1}: 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. -{Marathon Runners Narrative} Compute the p-value.Free

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Q 136Q 136

Marathon Runners
A researcher wants to study the average miles run per day for marathon runners.In testing the hypotheses: H

_{0}: 25 miles vs.H_{1}: 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. -{Marathon Runners Narrative} What can we conclude at the 5% significance level regarding the null hypothesis?Free

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Q 137Q 137

Marathon Runners
A researcher wants to study the average miles run per day for marathon runners.In testing the hypotheses: H

_{0}: 25 miles vs.H_{1}: 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. -{Marathon Runners Narrative} Develop a 95% confidence interval estimate of the population mean.Free

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Q 138Q 138

Marathon Runners
A researcher wants to study the average miles run per day for marathon runners.In testing the hypotheses: H

_{0}: 25 miles vs.H_{1}: 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. -{Marathon Runners Narrative} Explain briefly how to use the confidence interval to test the hypothesis.Free

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Q 139Q 139

Toaster Oven
An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W.From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W.A consumer group suspects the actual average is more than 250 W.They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W.
-{Toaster Oven Narrative} What is the parameter of interest in this situation?

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Q 140Q 140

Toaster Oven
An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W.From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W.A consumer group suspects the actual average is more than 250 W.They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W.
-{Toaster Oven Narrative} State the appropriate hypotheses for the consumer group to do their test.

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Q 141Q 141

Toaster Oven
An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W.From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W.A consumer group suspects the actual average is more than 250 W.They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W.
-{Toaster Oven Narrative} For a test with a level of significance of 0.05, determine the critical value.

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Q 142Q 142

Toaster Oven
An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W.From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W.A consumer group suspects the actual average is more than 250 W.They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W.
-{Toaster Oven Narrative} What is the value of the test statistic?

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Q 143Q 143

Toaster Oven
An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W.From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W.A consumer group suspects the actual average is more than 250 W.They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W.
-{Toaster Oven Narrative} Calculate the p-value of the test.

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Q 144Q 144

Toaster Oven
An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W.From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W.A consumer group suspects the actual average is more than 250 W.They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W.
-{Toaster Oven Narrative} What is the conclusion from the hypothesis test using = .05?

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Q 145Q 145

There is a direct relationship between the power of a test and the probability of a Type II error.

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True False

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True False

Q 147Q 147

For a given level of significance, if the sample size is increased, the power of the test will increase.

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True False

Q 148Q 148

If a sample size is increased at a given level, the probability of committing a Type II error is increased.

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True False

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True False

Q 150Q 150

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.

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True False

Q 151Q 151

For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

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True False

Q 152Q 152

The operating characteristic curve plots the values of (the probability of committing a Type II error) versus the values of the population mean .

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True False

Q 153Q 153

One way of expressing how well a test performs is to report its power--the probability of detecting a false null hypothesis.

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True False

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True False

Q 155Q 155

The power of a test is measured by its capability of:
A) rejecting a null hypothesis that is true.
B) not rejecting a null hypothesis that is true.
C) rejecting a null hypothesis that is false.
D) not rejecting a null hypothesis that is false.

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Multiple Choice

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Multiple Choice

Q 157Q 157

For a given level of significance, if the sample size increases, the probability of a Type II error will:
A) remain the same.
B) increase.
C) decrease.
D) be equal to 1.0 regardless of .

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Multiple Choice

Q 158Q 158

For a given sample size n, if the level of significance is decreased, the power of the test will:
A) increase.
B) decrease.
C) remain the same.
D) Not enough information to tell.

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Multiple Choice

Q 159Q 159

For a given level of significance , if the sample size n is increased, the probability of a Type II error will:
A) decrease.
B) increase.
C) remain the same.
D) Not enough information to tell.

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Multiple Choice

Q 160Q 160

If the probability of committing a Type I error for a given test is decreased, then for a fixed sample size n, the probability of committing a Type II error will:
A) decrease.
B) increase.
C) stay the same.
D) Not enough information to tell.

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Multiple Choice

Q 161Q 161

If we want to compute the probability of a Type II error, which of the following statements is false?
A) We need to know the significance level .
B) We need to know the sample size n.
C) We need to know the alternative value of the population mean .
D) All of these choices are true.

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Multiple Choice

Q 162Q 162

Which of the following statements is false regarding the operating characteristic (OC) curve?
A) The OC curve plots the values of versus the values of .
B) The OC curve plots the values of versus the values of .
C) The OC curve can be useful in selecting a sample size n.
D) None of these choices.

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Multiple Choice

Q 163Q 163

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will ____________________.

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Q 164Q 164

For a given level of significance, if the sample size is increased, the power of the test will ____________________.

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Q 165Q 165

To calculate the probability of a(n) ____________________ error you need to specify a value of other than the one given in the null hypothesis.

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Q 166Q 166

Probabilities for Type I and Type II errors are actually ____________________ probabilities.

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Q 167Q 167

By ____________________ the significance level, you increase the probability of a Type II error.

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Q 171Q 171

A(n) ____________________ characteristic curve plots the probability of a Type II error for various alternative values of ____________________.

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Q 172Q 172

As the sample size increases, the operating characteristic curves drop down to zero at a(n) ____________________ rate.

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Q 173Q 173

To test the hypotheses: H

_{0}: = 40 vs.H_{1}: 40, we draw a random sample of size 16 from a normal population whose standard deviation is 5.If we set = 0.01, find the probability of committing a Type II error when = 37.Free

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Q 174Q 174

Calculate the probability of a Type II error for the hypothesis test: H

_{0}: = 50 vs.H_{1}: > 50, given that = 55, = 0.05, = 10, and n = 16.Free

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Q 175Q 175

Rechargeable Batteries
A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses, H

_{0}: = 950 hours vs.H_{1}: 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -{Rechargeable Batteries Narrative} Calculate , the probability of a Type II error when = 1000 and = 0.10.Free

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Q 176Q 176

Rechargeable Batteries
A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses, H

_{0}: = 950 hours vs.H_{1}: 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -{Rechargeable Batteries Narrative} Calculate the power of the test when = 1000 and = 0.10.Free

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Q 177Q 177

Rechargeable Batteries
A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses, H

_{0}: = 950 hours vs.H_{1}: 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -{Rechargeable Batteries Narrative} Interpret the meaning of the power of the test.Free

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Q 178Q 178

Rechargeable Batteries
A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses, H

_{0}: = 950 hours vs.H_{1}: 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -{Rechargeable Batteries Narrative} Recalculate if n is increased from 25 to 40.Free

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Q 179Q 179

Rechargeable Batteries
A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses, H

_{0}: = 950 hours vs.H_{1}: 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -{Rechargeable Batteries Narrative} Review the results of the previous questions.What is the effect of increasing the sample size on the value of ?Free

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Q 180Q 180

Rechargeable Batteries
A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses, H

_{0}: = 950 hours vs.H_{1}: 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -{Rechargeable Batteries Narrative} Recalculate if is lowered from 0.10 to 0.05.Free

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Q 181Q 181

Rechargeable Batteries
A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses, H

_{0}: = 950 hours vs.H_{1}: 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -{Rechargeable Batteries Narrative} Review the results of the previous questions.What is the effect of decreasing the significance level on the value on ?Free

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Q 182Q 182

During the last energy crisis, a government official claimed that the average car owner refills the tank when there is more than 3 gallons left.To check the claim, 10 cars were surveyed as they entered a gas station.The amount of gas remaining before refill was measured and recorded as follows (in gallons): 3, 5, 3, 2, 3, 3, 2, 6, 4, and 1.Assume that the amount of gas remaining in tanks is normally distributed with a standard deviation of 1 gallon.Compute the probability of a Type II error and the power of the test if the true average amount of gas remaining in tanks is 3.5 gallons anda= 0.10.

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