# Quiz 10: One-Sample Tests of Hypothesis

Statistics

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Q 2Q 2

Hypothesis testing is a procedure that uses sample evidence and probability theory to decide whether to reject or fail to reject a hypothesis.

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Q 3Q 3

An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.

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Q 4Q 4

The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.

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Q 5Q 5

For a one-tailed test with a 0.05 level of significance,the critical z-statistic is 1.645,but the critical t-statistic is 1.96.

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Q 6Q 6

The level of significance is the probability of rejecting the null hypothesis when it is actually true.

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Q 8Q 8

A test statistic is a value computed from sample information that is used to test the null hypothesis.

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Q 9Q 9

If the null hypothesis is false and the researchers do not reject it,a Type I error has been made.

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Q 14Q 14

Assuming that the null hypothesis is true,a p-value is the probability of observing a sample value as extreme as,or more extreme than,the observed sample observation.

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True False

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Q 16Q 16

A null hypothesis makes a claim about a ________.
A)population parameter
B)sample statistic
C)sample mean
D)type II error

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Multiple Choice

Q 17Q 17

Define the level of significance.
A)It is the probability of a Type II error.
B)It is the probability of a Type I error.
C)It is a z-value of 1.96.
D)It is the beta error.

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Multiple Choice

Q 18Q 18

The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12)were selected at random and their lengths in millimeters recorded. The lengths (in millimeters)are 42,39,42,45,43,40,39,41,40,42,43,and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. If the computed t = −2.913,has there been a statistically significant change in the mean length of the bars?
A)Yes,because the computed t lies in the rejection region.
B)No,because the information given is not complete.
C)No,because the computed t lies in the area to the right of −2.718.
D)Yes,because 43 is greater than 41.5.

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Multiple Choice

Q 19Q 19

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed,a sample of nine boxes of cake mix gave these shelf lives (in days): 215,217,218,219,216,217,217,218,and 218. Using α = 0.025,has the shelf life of the cake mix increased?
A)Yes,because computed t is greater than the critical value.
B)Yes,because computed t is less than the critical value.
C)No,because computed t lies in the region of acceptance.
D)No,because 217.24 is quite close to 216.

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Multiple Choice

Q 20Q 20

A consumer products company wants to increase the absorption capacity of a sponge. Based on past data,the average sponge could absorb 3.5 ounces. After the redesign,the absorption amounts of a sample of sponges were (in ounces): 4.1,3.7,3.3,3.5,3.8,3.9,3.6,3.8,4.0,and 3.9. At the 0.01 level of significance,what is the decision rule to test if the new design increased the absorption of the sponge?
A)Reject the null hypothesis if computed t is less than 2.580.
B)Reject the null hypothesis if computed t is greater than 2.821.
C)Reject the null hypothesis if computed z is 1.96 or larger.
D)Reject the null hypothesis if computed t is less than 2.764.

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Multiple Choice

Q 21Q 21

A machine is set to fill the small-size packages of M&M candies with 56 candies per bag. A sample revealed three bags of 56,two bags of 57,one bag of 55,and two bags of 58. To test the hypothesis that the mean candies per bag is 56,how many degrees of freedom are there?
A)9
B)1
C)8
D)7

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Multiple Choice

Q 22Q 22

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed test and the researcher decided to use the 0.10 significance level. For what values of t will the null hypothesis not be rejected?
A)To the left of −1.282 or to the right of 1.282
B)To the left of −1.345 or to the right of 1.345
C)Between −1.761 and 1.761
D)To the left of −1.645 or to the right of 1.645

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Multiple Choice

Q 23Q 23

Using a 5% level of significance and a sample size of 25,what is the critical t-value for a null hypothesis,H

_{0}: µ ≤ 100? A)1.708 B)1.711 C)2.060 D)2.064Free

Multiple Choice

Q 24Q 24

To conduct a test of hypothesis with a small sample,we make an assumption that ________.
A)a larger computed value of t will be needed to reject the null hypothesis
B)the region of acceptance will be wider than for large samples
C)the confidence interval will be wider than for large samples
D)the population is normally distributed

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Multiple Choice

Q 25Q 25

What is a Type II error?
A)Failing to reject a false null hypothesis
B)Rejecting a false null hypothesis
C)Accepting a false alternate hypothesis
D)Rejecting a false alternate hypothesis

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Multiple Choice

Q 26Q 26

What statement do we make that determines if the null hypothesis is rejected?
A)Decision rule
B)Test statistic
C)Alternate hypothesis
D)Critical value

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Multiple Choice

Q 27Q 27

If the alternate hypothesis states that µ ≠ 4,000,where is the rejection region for the hypothesis test?
A)In both tails
B)In the lower or left tail
C)In the upper or right tail
D)In the center

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Multiple Choice

Q 28Q 28

What are the critical values for a two-tailed test with a 0.01 level of significance when n is large and the population standard deviation is known?
A)Above 1.960 and below -1.960
B)Above 1.645 and below -1.645
C)Above 2.576 and below -2.576
D)Above 1.000 and below -1.000

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Multiple Choice

Q 29Q 29

For a null hypothesis,H

_{0}: µ = 4,000,if the 1% level of significance is used and the z-test statistic is +6.00,what is our decision regarding the null hypothesis? A)Do not reject H_{0}. B)Reject H_{0}. C)Reject H_{1}. D)None of these answers apply.Free

Multiple Choice

Q 30Q 30

What is another name for the alternate hypothesis?
A)Null hypothesis
B)Hypothesis of no difference
C)Rejected hypothesis
D)Research hypothesis

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Multiple Choice

Q 31Q 31

For a two-tailed test with a 0.05 significance level,where is the rejection region when n is large and the population standard deviation is known?
A)Between ±1.960
B)Between ±1.645
C)Greater than +1.960 and less than −1.960
D)Greater than +1.645 and less than −1.645

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Multiple Choice

Q 32Q 32

What is the probability of making a Type II error if the null hypothesis is actually true?
A)α
B)1
C)0
D)0.05

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Multiple Choice

Q 33Q 33

Which symbol represents a test statistic used to test a hypothesis about a population mean?
A)α
B)β
C)μ
D)z

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Multiple Choice

Q 34Q 34

For an alternative hypothesis: µ > 6,700,where is the rejection region for the hypothesis test located?
A)In both tails
B)In the left or lower tail
C)In the right or upper tail
D)In the center

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Multiple Choice

Q 35Q 35

What are the critical z-values for a two-tailed hypothesis test if α = 0.01?
A)±1.960
B)±2.326
C)±2.576
D)±1.645

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Multiple Choice

Q 36Q 36

If the critical z-value for a hypothesis test equals 2.45,what value of the test statistic would provide the least chance of making a Type I error?
A)3.74
B)1.07
C)2.46
D)4.56

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Multiple Choice

Q 37Q 37

For a one-tailed hypothesis test,the critical z-value of the test statistic is −2.33. Which of the following is true about the hypothesis test?
A)α = 0.05 for a lower-tailed test
B)α = 0.01 for a lower-tailed test
C)α = 0.05 for an upper-tailed test
D)α = 0.01 for an upper-tailed test

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Multiple Choice

Q 38Q 38

If we reject the null hypothesis,what can we conclude subject to the probability,α?
A)Reject the null with a probability,α,of making a Type I error.
B)The alternative hypothesis is false.
C)The null hypothesis is true.
D)Both the null hypothesis and the alternative hypothesis are true.

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Multiple Choice

Q 39Q 39

Which of the following is not one of the six steps in the hypothesis testing procedure?
A)Formulate a decision rule.
B)State the null and alternate hypotheses.
C)Select a level for β.
D)Identify the test statistic.

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Multiple Choice

Q 40Q 40

In hypothesis testing,what is the level of significance?
A)The risk of rejecting the null hypothesis when it is true.
B)A value symbolized by the Greek letter α.
C)A value between 0 and 1.
D)It is selected before a decision rule can be formulated.
E)All of the answers apply.

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Multiple Choice

Q 41Q 41

The average cost of tuition and room and board for a small private liberal arts college is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What are the null and alternative hypotheses for this study?
A)H

_{0}: µ ≤ $9,000; H_{1}: µ > $9,000 B)H_{0}: µ ≥ $9,000; H_{1}: µ < $9,000 C)H_{0}: µ ≤ $8,500; H_{1}: µ > $8,500 D)H_{0}: µ ≥ $8,500; H_{1}: µ < $8,500Free

Multiple Choice

Q 42Q 42

The average cost of tuition plus room and board for a small private liberal arts college is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the critical z-value for this test?
A)+1.960
B)−1.960
C)+1.645
D)−1.645

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Multiple Choice

Q 43Q 43

The average cost of tuition plus room and board at for a small private liberal arts college is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the test statistic for this test?
A)±3.82
B)+0.204
C)−3.82
D)+3.82

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Multiple Choice

Q 44Q 44

The average cost of tuition plus room and board for a small private liberal arts college is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the p-value for this test?
A)0.0000
B)0.0124
C)0.0500
D)0.4938

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Multiple Choice

Q 45Q 45

The average cost of tuition plus room and board for a small private liberal arts college is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. Based on the computed test statistic or p-value,what is our decision about the average cost?
A)Equal to $8,500
B)Greater than $8,500
C)Less than $8,500
D)Not equal to $8,500

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Multiple Choice

Q 46Q 46

The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10,what is the decision rule?
A)Do not reject the null hypothesis if computed z lies between −1.645 and +1.645; otherwise,reject it.
B)Do not reject the null hypothesis if computed z is greater than 1.645; otherwise,reject it.
C)Do not reject the null hypothesis if computed z lies between −1.960 and +1.960; otherwise,reject it.
D)Reject the null hypothesis if computed z is below −1.960; otherwise,reject it.

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Multiple Choice

Q 47Q 47

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Which of the following is the alternate hypothesis?
A)H

_{1}: ≠ $50,000 B)H_{1}: µ ≠ $50,000 C)H_{1}: µ < $50,000 D)H_{1}: µ = $50,000Free

Multiple Choice

Q 48Q 48

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10,what is the critical value?
A)+1.645
B)−1.282
C)±1.282
D)±1.645

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Multiple Choice

Q 49Q 49

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. A sample of 100 welders is taken and the mean annual income of the sample is $50,350. If the level of significance is 0.05,what conclusion should be drawn?
A)Do not reject the null hypothesis as the test statistic is less than the critical value of z.
B)Do not reject the null hypothesis as the test statistic is less than the critical value of t.
C)Reject the null hypothesis as the test statistic is greater than the critical value of t.
D)Reject the null hypothesis as the test statistic is greater than the critical value of z.

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Multiple Choice

Q 50Q 50

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. A sample of 100 welders is taken and the mean annual income of the sample is $50,350. If the level of significance is 0.10,what conclusion should be drawn?
A)Do not reject the null hypothesis as the test statistic is less than the critical value of z.
B)Do not reject the null hypothesis as the test statistic is less than the critical value of t.
C)Reject the null hypothesis as the test statistic is greater than the critical value of t.
D)Reject the null hypothesis as the test statistic is greater than the critical value of z.

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Multiple Choice

Q 51Q 51

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. The null hypothesis is ________.
A)H

_{0}: µ = 6.6 B)H_{0}: µ ≥ 6.6 C)H_{0}: µ > 7.6 D)H_{0}: µ ≤ 7.6Free

Multiple Choice

Q 52Q 52

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. What is the alternate hypothesis?
A)H

_{1}: µ = 6.6 B)H_{1}: µ ≠ 6.6 C)H_{1}: µ ≥ 6.6 D)H_{1}: µ > 7.6Free

Multiple Choice

Q 53Q 53

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. What are the degrees of freedom?
A)7
B)8
C)6
D)6.6

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Multiple Choice

Q 54Q 54

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. If α = 0.05,what is the critical t-value?
A)−2.365
B)±1.96
C)±2.365
D)±2.447

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Multiple Choice

Q 55Q 55

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. What is the sample mean?
A)6.6
B)7.6
C)1.177
D)2.447

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Multiple Choice

Q 56Q 56

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. What is the sample variance?
A)1.177
B)6.6
C)1.386
D)7.6

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Multiple Choice

Q 57Q 57

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. What is the sample standard deviation?
A)1.177
B)1.188
C)1.386
D)1.090

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Multiple Choice

Q 58Q 58

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?
A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than 6.6 pounds.
C)Reject the null hypothesis and conclude the mean is lower than 6.6 pounds.
D)Cannot calculate because the population standard deviation is unknown.

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Multiple Choice

Q 59Q 59

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance?
A)Fail to reject the null hypothesis and conclude the mean is 6.6 pounds.
B)Reject the null hypothesis and conclude the mean is lower than 6.6 pounds.
C)Reject the null hypothesis and conclude the mean is greater than 6.6 pounds.
D)Cannot calculate because the population standard deviation is unknown.

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Multiple Choice

Q 60Q 60

The probability of a Type II error is directly related to ________.
A)α
B)the standard deviation
C)the Type I error
D)the difference between the hypothesized mean and the critical value of the sample mean

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Multiple Choice

Q 61Q 61

The probability of a Type II error is represented by ________.
A)α
B)β
C)the Type I error
D)σ

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Multiple Choice

Q 62Q 62

Consider a left-tailed test,where the p-value is found to be 0.10. If the sample size n for this test is 49,then the t-statistic will have a value of ________.
A)+1.677
B)−1.677
C)+1.299
D)−1.299

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Multiple Choice

Q 63Q 63

Consider a two-tailed test with a level of confidence of 80.30%. The z-value is ________.
A)2.58
B)1.29
C)0.85
D)1.96

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Multiple Choice

Q 64Q 64

Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05; therefore,the null hypothesis ________.
A)should not be rejected
B)must be rejected
C)may or may not be rejected depending on the square root of the sample size
D)is the same as the alternative hypothesis

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Multiple Choice

Q 65Q 65

Consider a right-tailed test (upper tail)and a sample size of 40 at the 95% confidence level. The value of t is ________.
A)+2.023
B)−2.023
C)−1.685
D)+1.685

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Multiple Choice

Q 66Q 66

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,400 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. The value of the test statistic is ________.
A)2.8
B)6,000
C)6,400
D)1.96

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Multiple Choice

Q 67Q 67

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.05,have sales increased as a result of the advertising campaign?
A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than $6,000 per day.
C)Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D)Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.

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Multiple Choice

Q 68Q 68

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.01,have sales increased as a result of the advertising campaign?
A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than $6,000 per day.
C)Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D)Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.

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Multiple Choice

Q 69Q 69

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.025,have sales increased as a result of the advertising campaign?
A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than $6,000 per day.
C)Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D)Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.

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Multiple Choice