Question 1

What is the level of significance?

Accepted Answer

A)  Probability of a Type II error 
B)  Probability of a Type I error 
C)  z-value of 1.96 
D)  Beta error 
A)  Probability of a Type II error 
B)  Probability of a Type I error 
C)  z-value of 1.96 
D)  Beta error

Question 2

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance.

Accepted Answer

A)  The null hypothesis is $\mu$ $\le$ 200. The alternate hypothesis is $\mu$ $\le$  200. 
B)  The null hypothesis is $\mu$ $\le$  200. The alternate hypothesis is $\mu$   > 200. 
C)  The null hypothesis is $\mu$   = 200. The alternate hypothesis is $\mu$ $\neq$  200. 
D)  The null hypothesis is $\mu$  > 200. The alternate hypothesis is $\mu$ $\le$  200 
E)  The null hypothesis is $\mu$ $\le$  220. The alternate hypothesis is $\mu$   > 220. 
A)  The null hypothesis is $\mu$ $\le$ 200. The alternate hypothesis is $\mu$ $\le$  200. 
B)  The null hypothesis is $\mu$ $\le$  200. The alternate hypothesis is $\mu$   > 200. 
C)  The null hypothesis is $\mu$   = 200. The alternate hypothesis is $\mu$ $\neq$  200. 
D)  The null hypothesis is $\mu$  > 200. The alternate hypothesis is $\mu$ $\le$  200 
E)  The null hypothesis is $\mu$ $\le$  220. The alternate hypothesis is $\mu$   > 220.

Question 3

The mean gross annual incomes of certified tack welders are normally distributed with the mean of $50,000 and a standard deviation of $4,000. The ship building association wishes to find out whether their tack welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. When tested at the 99% level, these are the results found with megastat:

Accepted Answer

A)  Since the p-value is 0.43 at this level of testing, there is insufficient evidence to say that the welders earn an income different from $50,000. 
B)  Since the p-value is 0.43 at this level of testing, there is sufficient evidence to say that the welders earn more than $50,000. 
C)  The p-value of 0.043 indicates that there is sufficient evidence to say that the welders earn more than $50,000. 
A)  Since the p-value is 0.43 at this level of testing, there is insufficient evidence to say that the welders earn an income different from $50,000. 
B)  Since the p-value is 0.43 at this level of testing, there is sufficient evidence to say that the welders earn more than $50,000. 
C)  The p-value of 0.043 indicates that there is sufficient evidence to say that the welders earn more than $50,000.

Question 4

If the alternative hypothesis states that $\mu$ > 6,700, what is the rejection region for the hypothesis test?

Accepted Answer

A)  Both tails 
B)  Lower tail 
C)  Upper tail 
D)  Center 
A)  Both tails 
B)  Lower tail 
C)  Upper tail 
D)  Center

Question 5

What is the probability of making a Type II error if the null hypothesis is actually true?

Accepted Answer

A)  $\alpha$ 
B)  1 
C)  0 
D)  0.05 
A)  $\alpha$ 
B)  1 
C)  0 
D)  0.05

Question 6

The Jamestown Steel Company manufactures and assembles desks and other office equipment at several plants. The weekly production of the Model A325 desk follows a normal probability distribution, with a mean of 200 and a standard deviation of 16. Recently, due to market expansion, new production methods have been introduced and new employees hired. The vice president of manufacturing would like to investigate whether there has been a change in the weekly production of the Model A325 desk. The mean number of desks produced last year (50 weeks, because the plant was shut down two weeks for vacation) is 203.5. Is the mean number of desks changed from 200? Test using the.05 significance level.

Accepted Answer

A)  Reject the null hypothesis; there is sufficient evidence to indicate an increase in the weekly production. 
B)  Unable to reject the null hypothesis; there is sufficient evidence to indicate a change in weekly production. 
C)  Unable to reject the null hypothesis; there is insufficient evidence to indicate an increase in weekly production. 
D)  Reject the null hypothesis; there is insufficient evidence to indicate a change in the weekly production. 
A)  Reject the null hypothesis; there is sufficient evidence to indicate an increase in the weekly production. 
B)  Unable to reject the null hypothesis; there is sufficient evidence to indicate a change in weekly production. 
C)  Unable to reject the null hypothesis; there is insufficient evidence to indicate an increase in weekly production. 
D)  Reject the null hypothesis; there is insufficient evidence to indicate a change in the weekly production.

Question 7

The average cost of tuition, room and board at community colleges is reported to be $8,500 per year, but a financial administrator believes that the average cost is higher. A study conducted using 150 community colleges showed that the average cost per year is $9,000 with a standard deviation of $1,200. Let $\alpha$ = 0.05. Given the following megastat printout, explain the meaning of the p-value.

Accepted Answer

A)  There is a 1.67% chance of getting these sample results if the null hypothesis is true. 
B)  There is a 16.7% chance of getting these sample results if the null hypothesis is true. 
C)  There is an incredibly small chance of getting these sample results if the null hypothesis is true; therefore we have strong evidence to support that college costs are more than $8,500. 
D)  There is an incredibly large chance of getting these sample results if the null hypothesis is true; therefore we are unable to reject the claim that college costs are $8,500. 
A)  There is a 1.67% chance of getting these sample results if the null hypothesis is true. 
B)  There is a 16.7% chance of getting these sample results if the null hypothesis is true. 
C)  There is an incredibly small chance of getting these sample results if the null hypothesis is true; therefore we have strong evidence to support that college costs are more than $8,500. 
D)  There is an incredibly large chance of getting these sample results if the null hypothesis is true; therefore we are unable to reject the claim that college costs are $8,500.

Question 8

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the level of significance is 2%, what is the critical value?

Accepted Answer

A)  2.05 
B)  -2.05 
C)  2.33 
D)  -2.33 
E)  1.96 
A)  2.05 
B)  -2.05 
C)  2.33 
D)  -2.33 
E)  1.96

Question 9

The average cost of tuition, room and board at community colleges is reported to be $8,500 per year with a standard deviation of $1,200, but a financial administrator believes that the average cost is higher. A study conducted using 150 community colleges showed that the average cost per year is $9,000. Let $\alpha$ = 0.05. Given the z-statistic is 5.1, what is our decision about the average cost?

Accepted Answer

A)  Equal to $8,500 
B)  Greater than $8,500 
C)  Less than $8,500 
D)  Not equal to $8,500 
A)  Equal to $8,500 
B)  Greater than $8,500 
C)  Less than $8,500 
D)  Not equal to $8,500

Question 10

i. To set up a decision rule, the sampling distribution is divided into two regions-a region of non-rejection and a region where the null hypothesis is rejected. ii. A test statistic is a value determined from sample information collected to test the null hypothesis.
iii. If the null hypothesis is true and the researchers do not reject it, then a correct decision has been made.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (i) and (ii) are correct statements but not (iii). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (i) and (ii) are correct statements but not (iii). 
E)  (i), (ii), and (iii) are all false statements.

Question 11

One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire. The warranty is for 40,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles with a standard deviation of 15,000 miles. A sample 49 tires revealed that the mean number of miles is 45,000 miles. Test the hypothesis with a 0.05 significance level.

Accepted Answer

A) The decision rule is to reject if Z > 1.645. The calculated value of z is +2.33. B) The decision rule is to reject if Z 1.96. The calculated value of z is +2.33. D) The decision rule is to reject if Z < 1.96. The calculated value of z is +2.33. A) The decision rule is to reject if Z > 1.645. The calculated value of z is +2.33. B) The decision rule is to reject if Z 1.96. The calculated value of z is +2.33. D) The decision rule is to reject if Z < 1.96. The calculated value of z is +2.33.

Question 12

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the sample proportion?

Accepted Answer

A)  0.41 
B)  0.36% 
C)  0.41% 
D)  0.36 
A)  0.41 
B)  0.36% 
C)  0.41% 
D)  0.36

Question 13

What do we call the statement that determines if the null hypothesis is rejected?

Accepted Answer

A)  Decision rule 
B)  Test statistic 
C)  Alternate hypothesis 
D)  Critical value 
A)  Decision rule 
B)  Test statistic 
C)  Alternate hypothesis 
D)  Critical value

Question 14

The mean gross annual incomes of certified tack welders are normally distributed with the mean of $50,000 and a standard deviation of $4,000. The ship building association wishes to find out whether their tack 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?

Accepted Answer

A)  1.65 
B)  2.58 
C)  1.28 
D)   $\pm$1.28 
E)   $\pm$1.645 
A)  1.65 
B)  2.58 
C)  1.28 
D)   $\pm$1.28 
E)   $\pm$1.645

Question 15

i. The level of significance is the risk we assume of rejecting the null hypothesis when it is actually true. ii. There is only one level of significance that is applied to all studies involving sampling.
iii. The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (i) and (ii) are correct statements but not (iii). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (i) and (ii) are correct statements but not (iii). 
E)  (i), (ii), and (iii) are all false statements.

Question 16

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if $\alpha$ = 0.01?

Accepted Answer

A)  2.58 
B)  2.33 
C)   $\pm$ 2.58 
D)  -2.33 
A)  2.58 
B)  2.33 
C)   $\pm$ 2.58 
D)  -2.33

Question 17

The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available" is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?

Accepted Answer

A)  Do no reject the null hypothesis because -0.866 lies in the region between 0 and -2.33 
B)  Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.58 
C)  Reject the null hypothesis because 37% is less than 40% 
D)  Do not reject the null hypothesis because 37% lies in the area between 0% and 40% 
A)  Do no reject the null hypothesis because -0.866 lies in the region between 0 and -2.33 
B)  Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.58 
C)  Reject the null hypothesis because 37% is less than 40% 
D)  Do not reject the null hypothesis because 37% lies in the area between 0% and 40%

Question 18

One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire. The warranty is for 40,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles with a standard deviation of 15,000 miles. A sample 49 tires revealed that the mean number of miles is 45,000 miles. Test the hypothesis with a 0.05 significance level.

Accepted Answer

A)  At a 5% level of significance, our decision is to reject the null hypothesis. The tires last more than 40 000 miles. 
B)  At a 5% level of significance, our decision is to accept the null hypothesis. The tires last 40,000 miles. 
C)  At a 5% level of significance, we should have used the t-test, rather than the z-test. 
A)  At a 5% level of significance, our decision is to reject the null hypothesis. The tires last more than 40 000 miles. 
B)  At a 5% level of significance, our decision is to accept the null hypothesis. The tires last 40,000 miles. 
C)  At a 5% level of significance, we should have used the t-test, rather than the z-test.

Question 19

i. The first step in testing a hypothesis is to state the decision rule. ii. To prevent bias, the level of significance is selected before setting up the decision rule and sampling the population.
iii. The fifth and final step in testing a hypothesis is taking a sample and, based on the decision rule, deciding if the null hypothesis should be rejected.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (i) and (ii) are correct statements but not (iii). 
E)  (ii) and (iii) are correct statements but not (i). 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (i) and (ii) are correct statements but not (iii). 
E)  (ii) and (iii) are correct statements but not (i).

Question 20

The dean of a business school claims that the average starting salary of its graduates is more than $50,000. It is known that the population standard deviation is $10,000. Sample data on the starting salaries of 25 randomly selected recent graduates yielded a mean of $52,000. What is the value of the sample test statistic?

Accepted Answer

A)  z = 1.0 
B)  t = 7.2 
C)  t = 5.04 
D)  t = 1.22 
A)  z = 1.0 
B)  t = 7.2 
C)  t = 5.04 
D)  t = 1.22

What is the level of significance?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance.

If the alternative hypothesis states that $\mu$ > 6,700, what is the rejection region for the hypothesis test?

What is the probability of making a Type II error if the null hypothesis is actually true?

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the level of significance is 2%, what is the critical value?

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the sample proportion?

What do we call the statement that determines if the null hypothesis is rejected?

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if $\alpha$ = 0.01?

The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available" is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

Exam 9: One-Sample Tests of Hypothesis

What is the level of significance?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance.

If the alternative hypothesis states that μ\muμ > 6,700, what is the rejection region for the hypothesis test?

What is the probability of making a Type II error if the null hypothesis is actually true?

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the level of significance is 2%, what is the critical value?

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the sample proportion?

What do we call the statement that determines if the null hypothesis is rejected?

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if α\alphaα = 0.01?

The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available" is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

If the alternative hypothesis states that $\mu$ > 6,700, what is the rejection region for the hypothesis test?

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if $\alpha$ = 0.01?