Deck 8: Introduction to Hypothesis Testing

Question 1

Which of the following represents the probability of a Type II error?​

A)​µ
B)​σ
C)​β
D)​α

Answer 1

​β

Question 2

If α is held constant at .05,what is the impact of changing the sample size on the critical region and the risk of a Type I error?​

A)​As sample size increases, the critical region expands and the risk of a Type I error increases.
B)​As sample size increases, the critical region shrinks and the risk of a Type I error increases.
C)​As sample size increases, the critical region expands and the risk of a Type I error decreases.
D)​As the sample size increases, the critical region, and the risk of a Type I error remain unchanged.

Answer 2

​As the sample size increases, the critical region, and the risk of a Type I error remain unchanged.

Question 3

Which of the following correctly describes the effect of increasing the alpha level (for example,from .01 to .05)?​

A)​Increase the likelihood of rejecting H₀ and increase the risk of a Type I error.
B)​Decrease the likelihood of rejecting H₀ and increase the risk of a Type I error.
C)​Increase the likelihood of rejecting H₀ and decrease the risk of a Type I error.
D)​Decrease the likelihood of rejecting H₀ and decrease the risk of a Type I error.

Answer 3

​Increase the likelihood of rejecting H₀ and increase the risk of a Type I error.

Question 4

Decreasing the alpha level from α = .05 to α = .01 ____.​

A)​increases the probability of a Type I error
B)​increases the size of the critical region
C)​increases the probability that the sample will fall into the critical region
D)​decreases the probability of a Type I error

Question 5

A researcher conducts a hypothesis test to evaluate the effect of a treatment.The hypothesis test produces a z-score of z = 2.37.Assuming that the researcher is using a two-tailed test,what decision should be made?​

A)​The researcher should reject the null hypothesis with α = .05 but not with α = .01.
B)​The researcher should reject the null hypothesis with either α = .05 or α = .01.
C)​The researcher should fail to reject H₀ with either α = .05 or α = .01.
D)​The researcher should ignore the results.

Question 6

Which of the following accurately describes the critical region?​

A)​Outcomes with a very low probability if the null hypothesis is true
B)​Outcomes with a high probability if the null hypothesis is true
C)​Outcomes with a very low probability whether or not the null hypothesis is true
D)​Outcomes with a high probability whether or not the null hypothesis is true

Question 7

Which of the following is an accurate definition of a Type II error?​​

A)​Rejecting a false null hypothesis
B)​Rejecting a true null hypothesis
C)​Failing to reject a false null hypothesis
D)​Failing to reject a true null hypothesis

Question 8

A two-tailed hypothesis test is being used to evaluate a treatment effect with α = .05.If the sample data produce a z-score of z = 2.24,then what is the correct decision?​

A)​Reject the null hypothesis and conclude that the treatment has no effect.
B)​Reject the null hypothesis and conclude that the treatment has an effect.
C)​Fail to reject the null hypothesis and conclude that the treatment has no effect.
D)​Fail to reject the null hypothesis and conclude that the treatment has an effect.

Question 9

What is measured by the numerator of the z-score test statistic?​

A)​The average distance between M and µ that would be expected if H₀ was true
B)​The actual distance between M and µ
C)​The position of the sample mean relative to the critical region
D)​Whether or not there is a significant difference between M and µ

Question 10

What is the relationship between the alpha level,the size of the critical region,and the risk of a Type I error?​

A)​As the alpha level increases, the size of the critical region increases and the risk of a Type I error increases.
B)​As the alpha level increases, the size of the critical region increases and the risk of a Type I error decreases.
C)​As the alpha level increases, the size of the critical region decreases and the risk of a Type I error increases.
D)​As the alpha level increases, the size of the critical region decreases and the risk of a Type I error decreases.

Question 11

A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores.The hypothesis test produces a z-score of z = 2.37.If the researcher is using a one-tailed test,what is the correct statistical decision?​

A)​Reject the null hypothesis with α = .05 but not with α = .01.
B)​Reject the null hypothesis with either α = .05 or α = .01.
C)​Fail to reject the null hypothesis with either α = .05 or α = .01.
D)​This cannot be answered without additional information.

Question 12

Even if a treatment has no effect,it is still possible to obtain an extreme sample mean that is very different from the population mean.What outcome is likely if this happens?​

A)​Reject H₀ and make a Type I error.
B)​Correctly reject H_0.
C)​Fail to reject H₀ and make a Type II error.
D)​Correctly fail to reject H_0.

Question 13

Which of the following accurately describes a hypothesis test?​

A)​A descriptive technique that allows researchers to describe a sample
B)​A descriptive technique that allows researchers to describe a population
C)​An inferential technique that uses the data from a sample to draw inferences about a population
D)​An inferential technique that uses information about a population to make predictions about a sample

Question 14

A sample of n = 25 individuals is selected from a population with µ = 80 and a treatment is administered to the sample.What is expected if the treatment has no effect?​

A)​The sample mean should be very different from 80 and should lead you to reject the null hypothesis.
B)​The sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis.
C)​The sample mean should be close to 80 and should lead you to reject the null hypothesis.
D)​The sample mean should be close 80 and should lead you to fail to reject the null hypothesis.

Question 15

What is measured by the denominator of the z-score test statistic?​

A)​The average distance between M and µ that would be expected if H₀ was true
B)​The actual distance between M and µ
C)​The position of the sample mean relative to the critical region
D)​Whether or not there is a significant difference between M and µ

Question 16

Which of the following is directly addressed by the null hypothesis?​

A)​The population before treatment
B)​The population after treatment
C)​The sample before treatment
D)​The sample after treatment

Question 17

By selecting a larger alpha level,a researcher is ____.​

A)​attempting to make it more difficult to reject H₀
B)​less able to detect a treatment effect
C)​increasing the risk of a Type I error
D)​decreasing the risk of a Type I error

Question 18

The critical boundaries for a hypothesis test are z = +1.96 and 1.96.If the z-score for the sample data is z = 1.90,then what is the correct statistical decision?

A)​Fail to reject H₁
B)​Fail to reject H₀
C)​Reject H₁
D)​Reject H₀

Question 19

Which of the following is an accurate definition of a Type I error?​

A)Rejecting a false null hypothesis​
B)​Rejecting a true null hypothesis
C)​Failing to reject a false null hypothesis
D)​Failing to reject a true null hypothesis

Question 20

Even if a treatment has an effect,it is still possible to obtain a sample mean that is very similar to the original population mean.What outcome is likely if this happens?​

A)​Reject H₀ and make a Type I error.
B)​Correctly reject H_0.
C)​Fail to reject H₀ and make a Type II error.
D)​Correctly fail to reject H_0.

Question 21

Which of the following is an accurate definition for the power of a statistical test?​

A)​The probability of rejecting a true null hypothesis
B)​The probability of supporting true null hypothesis
C)​The probability of rejecting a false null hypothesis
D)​The probability of supporting a false null hypothesis

Question 22

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If the researcher obtains a sample mean of M = 88,given the same alpha level,which combination of factors is most likely to result in rejecting the null hypothesis?​

A)​σ = 5 and n = 25
B)​σ = 5 and n = 50
C)​σ = 10 and n = 25
D)​σ = 10 and n = 50

Question 23

A sample of n = 16 individuals is selected from a population with μ = 60 and σ = 6 and a treatment is administered to the sample.After treatment,the sample mean is M = 63.What is the value of Cohen's d for this sample?​

A)​0.33
B)​0.50
C)​2.00
D)​3.00

Question 24

If a hypothesis test is found to have power = 0.70,then what is the probability that the test will result in a Type II error?​

A)​0.30
B)​0.70
C)​p > 0.70
D)​0.40

Question 25

When is there a risk of a Type II error?​

A)​Whenever H₀ is rejected
B)​Whenever H₁ is rejected
C)​Whenever the decision is "fail to reject H₀"
D)​The risk of a Type II error is independent of the decision from a hypothesis test.

Question 26

a researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population which is known to have a mean of ? = 80.The results will be examined using a one-tailed hypothesis test.Which of the following is the correct statement of the null hypothesis??

A) $$\mu > 80$$
B) $$\mu \geq 80$$
C) $$\mu < 80$$
D) $$\mu \leq 80$$

Question 27

When is there a risk of a Type I error?​

A)​Whenever H₀ is rejected
B)​Whenever H₁ is rejected
C)​Whenever the decision is "fail to reject H₀"
D)​The risk of a Type I error is independent of the decision from a hypothesis test.

Question 28

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If the researcher obtains a sample mean of M = 88,given the same sample size,which combination of factors is most likely to result in rejecting the null hypothesis?​

A)​σ = 5 and α = .01
B)​σ = 5 and α = .05
C)​σ = 10 and α = .01
D)​σ = 10 and α = .05

Question 29

Which of the following will increase the power of a statistical test?​

A)​Change α from .05 to .01
B)​Change from a one-tailed test to a two-tailed test
C)​Change the sample size from n = 25 to n = 100
D)​None of the other three options will increase the power.

Question 30

Which of the following accurately describes the effect of increasing the sample size?​

A)​Increases the standard error and has no effect on the risk of a Type I error
B)​Decreases the standard error and has no effect on the risk of a Type I error
C)​Increases the risk of a Type I error and has no effect on the standard error
D)​Decreases the risk of a Type I error and has no effect on the standard error

Question 31

If a treatment has a very small effect,then what is a likely outcome for a hypothesis test evaluating the treatment?​

A)​A Type I error
B)​A Type II error
C)​Correctly reject the null hypothesis
D)​Correctly fail to reject the null hypothesis

Question 32

Which combination of factors will increase the chances of rejecting the null hypothesis?​

A)​A large standard error and a large alpha level
B)​A large standard error and a small alpha level
C)​A small standard error and a large alpha level
D)​A small standard error and a small alpha level

Question 33

Under what circumstances can a very small treatment effect still be significant?​

A)If the sample size (n) is very large​
B)​If the sample standard deviation (σ) is very large
C)​If the standard error of M (σ _M) is very large
D)​All of the other three factors will result in a significant treatment effect.

Question 34

What is the consequence of a Type I error?​

A)​Concluding that a treatment has an effect when it really does
B)​Concluding that a treatment has no effect when it really has no effect
C)​Concluding that a treatment has no effect when it really does
D)​Concluding that a treatment has an effect when it really has no effect

Question 35

A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population.If the researcher uses a one-tailed test with a = .01,then which of the following correctly identifies the critical region?​

A)​z > 2.33
B)​z > 2.58
C)​z < 2.33
D)​z < 2.58

Question 36

A researcher expects a treatment to produce an increase in the population mean.The treatment is evaluated using a one tailed hypothesis test,and the test produces z = +1.85.Based on this result,what is the correct statistical decision?​

A)​The researcher should reject the null hypothesis with α = .05 but not with α = .01.
B)​The researcher should reject the null hypothesis with either α = .05 or α = .01.
C)​The researcher should fail to reject H₀ with either α = .05 or α = .01.
D)​The researcher should change α.

Question 37

What is the consequence of a Type II error?​

A)​Concluding that a treatment has an effect when it really does
B)​Concluding that a treatment has no effect when it really has no effect
C)​Concluding that a treatment has no effect when it really does
D)​Concluding that a treatment has an effect when it really has no effect

Question 38

A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of µ = 80 and a standard deviation of σ = 12.After treatment,the effect size is measured by computing Cohen's d,and a value of d = 0.50 is obtained.Based on this information,what is the mean for the treated sample?​

A)​M = 6
B)​M = 82
C)​M = 86
D)​This cannot be answered without knowing the sample size.

Question 39

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If a hypothesis test is used to evaluate the effect of the treatment,which combination of factors is most likely to result in rejecting the null hypothesis?​

A)​A sample mean near 80 for a small sample
B)​A sample mean near 80 for a large sample
C)​A sample mean much different than 80 for a small sample
D)​A sample mean much different than 80 for a large sample

Question 40

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If a hypothesis test is used to evaluate the effect of the treatment,which combination of factors is most likely to result in rejecting the null hypothesis?​

A)​A sample mean near 80 with α = .05
B)​A sample mean near 80 with α = .01
C)​A sample mean much different than 80 with α = .05
D)​A sample mean much different than 80 with α = .01

Question 41

In general,the null hypothesis states that the treatment has no effect on the population parameter being studied.​

Question 42

In a research report,the notation p < .05 indicates that the probability of a Type I error is less than .05.

Question 43

The alpha level determines the risk of a Type I error.

Question 44

A Type I error occurs when a researcher concludes that a treatment has an effect but,in fact,the treatment has no effect.

Question 45

Most researchers would like the hypothesis test to reject the null hypothesis.

Question 46

If the research prediction is that the treatment will decrease scores,then the critical region for a directional test will be in the left-hand tail.

Question 47

If the sample data are in the critical region with α = .05,then the same sample data would still be in the critical region if α were changed to .01.

Question 48

The null hypothesis states that the sample mean (after treatment)is equal to the original population mean (before treatment).​

Question 49

If a hypothesis test leads to rejecting the null hypothesis,it means that the data did not provide enough evidence to conclude that the treatment has an effect.

Question 50

The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.

Question 51

A researcher administers a treatment to a sample from a population with a mean of m = 60.If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect,then the null hypothesis states that m 60.

Question 52

A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis.

Question 53

A Type I error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis.

Question 54

A researcher is evaluating a treatment that is expected to increase scores.If a one-tailed test with a = .05 is used,then the critical region consists of z-scores greater than 1.65.

Question 55

You can reduce the risk of a Type I error by using a larger sample.

Question 56

A research report includes the statement,z = 2.13,p < .05.For this hypothesis test,the used null hypothesis is rejected using an alpha level of α = .05.

Question 57

If a research report includes the term significant result,it means that the null hypothesis was rejected.

Question 58

The null hypothesis is stated in terms of the population,even though the data come from a sample.

Question 59

If the sample data are in the critical region with α = .01,then the same sample data would still be in the critical region if α were changed to .05.

Question 60

There is always a possibility that the decision reached in a hypothesis test is incorrect.

Question 61

A researcher would like to determine whether a new tax on cigarettes has had any effect on people's behavior.During the year before the tax was imposed,stores located in rest areas on the state thruway reported selling an average of µ = 410 packs per day with σ = 60.The distribution of daily sales was approximately normal.For a sample of n = 9 days following the new tax,the researcher found an average of M = 386 packs per day for the same stores.
a. Is the sample mean sufficient to conclude that there was a significant change in cigarette purchases after the new tax. Use a two-tailed test with α = .05.
b. If the population standard deviation was σ = 30, is the result sufficient to conclude that there is a significant difference?
c. Explain why the two tests lead to different outcomes.

Question 62

If other factors such as sample size,alpha level,and population standard deviation are held constant,the larger the size of the treatment effect,the greater the power of the hypothesis test.

Question 63

If the power for a hypothesis test is calculated to be 0.80,then for same test,the probability of a Type II error is 0.20.

Question 64

The power of a hypothesis test is the probability that the sample mean will be in the critical region if the treatment has an effect.

Question 65

A researcher selects a sample of n = 25 from a normal population with µ = 40 and σ = 10.If the treatment is expected to increase scores by 3 points,what is the power of a two-tailed hypothesis test using α = .05?

Question 66

If all other factors are held constant,increasing the sample size from n = 25 to n = 100 will increase the power of a statistical test.

Question 67

A measure of effect size is intended to provide a measurement of the absolute magnitude of a treatment effect.

Question 68

One of the simplest and most direct methods for measuring effect size is Cohen's
d.

Question 69

A significant treatment effect does not necessarily indicate a large treatment effect.

Question 70

Define the critical region for a hypothesis test,and explain how the critical region is related to the alpha level.

Question 71

A researcher is testing the effectiveness of a new herbal supplement that claims to improve physical fitness.A sample of n = 16 college students is obtained and each student takes the supplement daily for six weeks.At the end of the 6-week period,each student is given a standardized fitness test and the average score for the sample is M = 39.For the general population of college students,the distribution of test scores is normal with a mean of µ = 35 and a standard deviation of σ = 12.Do students taking the supplement have significantly better fitness scores? Use a one-tailed test with α = .05.

Question 72

A directional hypothesis test is also referred to as a one-tailed test.

Question 73

Some researchers claim that herbal supplements such as ginseng or ginkgo biloba enhance human memory.To test this claim,a researcher selects a sample of n = 25 college students.Each student is given a ginkgo biloba supplement daily for six weeks and then all the participants are given a standardized memory test.For the population,scores on the test are normally distributed with μ = 70 and σ = 15.The sample of n = 25 students had a mean score of M = 75.
a. Are the data sufficient to that the herb has a significant effect on memory? Use a two-tailed test with α = .05.
b. Compute Cohen's d for this study.

Question 74

A researcher administers a treatment to a sample of n = 16 selected from a population with m = 40 and s = 8.If the sample mean after treatment is M = 42,then Cohen's d = 1.00.

Question 75

The value obtained for Cohen's d is independent of the sample size.

Question 76

The term error is used in two different ways in hypothesis testing: a Type I error (or Type II)and the standard error.
a. What can a researcher do to influence the size of the standard error? Does this action have any effect on the probability of a Type I error?
b. What can a researcher do to influence the probability of a Type I error? Does this action have any effect on the size of the standard error?