Question 1

What are the two rejection areas in using a two-tailed test and the 0.01 level of significance when the population standard deviation is known?

Accepted Answer

A)  Above 1.96 and below -1.96 
B)  Above 1.65 and below -1.65 
C)  Above 2.58 and below -2.58 
D)  Above 1.00 and below -1.00 
A)  Above 1.96 and below -1.96 
B)  Above 1.65 and below -1.65 
C)  Above 2.58 and below -2.58 
D)  Above 1.00 and below -1.00

Question 2

What does z equal for an $\alpha$ = 0.01 and a lower level test?

Accepted Answer

A)  +2.33 
B)  -2.33 
C)  +2.58 
D)  -2.58 
A)  +2.33 
B)  -2.33 
C)  +2.58 
D)  -2.58

Question 3

i. If the critical values of the test statistic z are  $\pm$1.96, they are the dividing points between the areas of rejection and non-rejection. ii. The probability of a Type I error is also referred to as alpha.
iii. A Type I error is the probability of rejecting a true null hypothesis.

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 4

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.

Accepted Answer

A)  The z-statistic is -2.25 
B)  The z-statistic is 2.25 
C)  The z-statistic is -1.00 
D)  The z-statistic is 1.00 
A)  The z-statistic is -2.25 
B)  The z-statistic is 2.25 
C)  The z-statistic is -1.00 
D)  The z-statistic is 1.00

Question 5

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 null hypothesis?

Accepted Answer

A)  p = 0.36 
B)  p = 0.41 
C)  p $\neq$ 0.36 
D)  $\mu$ = 0.41 
A)  p = 0.36 
B)  p = 0.41 
C)  p $\neq$ 0.36 
D)  $\mu$ = 0.41

Question 6

Which of the following does NOT hold true for the t distribution?

Accepted Answer

A)  Confidence intervals will be wider than for large samples. 
B)  The region of acceptance will be larger than for large samples. 
C)  A larger computed t value will be needed to reject the null hypothesis than for large samples using z. 
D)  There is only one t distribution. 
A)  Confidence intervals will be wider than for large samples. 
B)  The region of acceptance will be larger than for large samples. 
C)  A larger computed t value will be needed to reject the null hypothesis than for large samples using z. 
D)  There is only one t distribution.

Question 7

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the z-statistic?

Accepted Answer

A)  0.025 
B)  0.278 
C)  -1.65 
D)  1.67 
A)  0.025 
B)  0.278 
C)  -1.65 
D)  1.67

Question 8

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. Which of the following is the alternate hypothesis?

Accepted Answer

A)  p $\neq$ $50,000 
B)  $\mu$ $\neq$ $50,000 
C)  $\mu$ < $50,000 
D)  $\mu$ = $50,000 
E)  p = $50,000 
A)  p $\neq$ $50,000 
B)  $\mu$ $\neq$ $50,000 
C)  $\mu$ < $50,000 
D)  $\mu$ = $50,000 
E)  p = $50,000

Question 9

i. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt that the null hypothesis is true. ii. A test statistic is a value determined from sample information collected to test the null hypothesis.
iii. The region or area of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.

Accepted Answer

A)  (ii) and (iii) are correct statements but not (i). 
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)  (ii) and (iii) are correct statements but not (i). 
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 10

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 produced different from 200? Test using the.01 significance level. i. The alternate hypothesis is $\mu$ $\le$ 200.
ii. It is appropriate to use the z-test.
iii. The decision rule is: if the computed value of the test statistic is not between -2.58 and 2.58, reject the null hypothesis.

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)  (ii) and (iii) are correct statements but not (i). 
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)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 11

To conduct a test of hypothesis with a small sample, we need to be able to make the following assumption that:

Accepted Answer

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. 
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.

Question 12

The printout below refers to the weekly closing stock prices for Air Canada on 20 randomly selected weeks in 2000. Using a 5% level of significance, can you say that the average Air Canada stock price was less than $19.00?

Accepted Answer

A)  Fail to reject the null hypothesis and conclude the mean stock price was $19.00. 
B)  Since the P-value is less than the selected alpha, reject the null hypothesis and conclude the mean stock price was lower than $19.00. 
C)  Since the P-value is more than the selected alpha, reject the null hypothesis and conclude the mean stock price was more than $19.00. 
D)  Since the P-value is less than the selected alpha, reject the null hypothesis and conclude the mean stock price was different from $19.00. 
E)  Since the confidence interval doesn't contain the value $19.00, reject the null hypothesis and conclude that the mean stock price is different from $19.00. 
A)  Fail to reject the null hypothesis and conclude the mean stock price was $19.00. 
B)  Since the P-value is less than the selected alpha, reject the null hypothesis and conclude the mean stock price was lower than $19.00. 
C)  Since the P-value is more than the selected alpha, reject the null hypothesis and conclude the mean stock price was more than $19.00. 
D)  Since the P-value is less than the selected alpha, reject the null hypothesis and conclude the mean stock price was different from $19.00. 
E)  Since the confidence interval doesn't contain the value $19.00, reject the null hypothesis and conclude that the mean stock price is different from $19.00.

Question 13

The mean weight of newborn infants at a community hospital is said to be 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 $\alpha$ = 0.05, what is the critical t value?

Accepted Answer

A)  -2.365 
B)   $\pm$ 1.96 
C)   $\pm$ 2.365 
D)   $\pm$ 2.447 
E)  -2.447 
A)  -2.365 
B)   $\pm$ 1.96 
C)   $\pm$ 2.365 
D)   $\pm$ 2.447 
E)  -2.447

Question 14

i. An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected. ii. The level of significance is the risk we assume of rejecting the null hypothesis when it is actually true.
iii. There is only one level of significance that is applied to all studies involving sampling.

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 15

i. The probability of a Type I error is also referred to as alpha. ii. A Type I error is the probability of accepting a true null hypothesis.
iii. A Type I error is the probability of rejecting a true null hypothesis.

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

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. The t-value is calculated to be 5.77. At the 0.01 level of significance, what is your decision?

Accepted Answer

A)  You reject the null hypothesis, and agree that the average monthly bill exceeds $200. 
B)  You have insufficient evidence to reject the null hypothesis. 
C)  You reject the alternate hypothesis and agree that the average monthly bill is less than $200. 
D)  You should have used the z-test. 
A)  You reject the null hypothesis, and agree that the average monthly bill exceeds $200. 
B)  You have insufficient evidence to reject the null hypothesis. 
C)  You reject the alternate hypothesis and agree that the average monthly bill is less than $200. 
D)  You should have used the z-test.

Question 17

i. Two examples of a hypothesis are: 1) mean monthly income from all sources for senior citizens is $841 and
2) twenty percent of juvenile offenders ultimately are caught and sentenced to prison.
ii. Since there is more variability in sample means computed from smaller samples, we have more confidence in the resulting estimates and are less apt to reject null hypothesis.
iii. The test statistic for a problem where the population standard deviation is unknown is the Student's t distribution.

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 18

i. Two examples of a hypothesis are: 1) mean monthly income from all sources for senior citizens is $841 and
2) twenty percent of juvenile offenders ultimately are caught and sentenced to prison.
ii. Hypothesis testing is a procedure based on sample evidence and probability theory to decide whether the hypothesis is a reasonable statement.
iii. Since there is more variability in sample means computed from smaller samples, we have more confidence in the resulting estimates and are less apt to reject null hypothesis.

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 19

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 25 and an unknown population standard deviation?

Accepted Answer

A)  1.708 
B)  1.711 
C)  2.060 
D)  2.064 
A)  1.708 
B)  1.711 
C)  2.060 
D)  2.064

Question 20

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two-tailed test at the 0.10 significance level is to be used. For what value of t will the null hypothesis be rejected?

Accepted Answer

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)  To the left of-1.761 or to the right of 1.761 
D)  To the left of-1.645 or to the right of 1.645 
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)  To the left of-1.761 or to the right of 1.761 
D)  To the left of-1.645 or to the right of 1.645

What are the two rejection areas in using a two-tailed test and the 0.01 level of significance when the population standard deviation is known?

What does z equal for an $\alpha$ = 0.01 and a lower level test?

i. If the critical values of the test statistic z are $\pm$ 1.96, they are the dividing points between the areas of rejection and non-rejection. ii. The probability of a Type I error is also referred to as alpha. iii. A Type I error is the probability of rejecting a true null hypothesis.

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.

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 null hypothesis?

Which of the following does NOT hold true for the t distribution?

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the z-statistic?

To conduct a test of hypothesis with a small sample, we need to be able to make the following assumption that:

The printout below refers to the weekly closing stock prices for Air Canada on 20 randomly selected weeks in 2000. Using a 5% level of significance, can you say that the average Air Canada stock price was less than $19.00?

The mean weight of newborn infants at a community hospital is said to be 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 $\alpha$ = 0.05, what is the critical t value?

i. The probability of a Type I error is also referred to as alpha. ii. A Type I error is the probability of accepting a true null hypothesis. iii. A Type I error is the probability of rejecting a true null hypothesis.

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 25 and an unknown population standard deviation?

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two-tailed test at the 0.10 significance level is to be used. For what value of t will the null hypothesis be rejected?

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 are the two rejection areas in using a two-tailed test and the 0.01 level of significance when the population standard deviation is known?

What does z equal for an α\alphaα = 0.01 and a lower level test?

i. If the critical values of the test statistic z are ±\pm± 1.96, they are the dividing points between the areas of rejection and non-rejection. ii. The probability of a Type I error is also referred to as alpha. iii. A Type I error is the probability of rejecting a true null hypothesis.

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.

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 null hypothesis?

Which of the following does NOT hold true for the t distribution?

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the z-statistic?

To conduct a test of hypothesis with a small sample, we need to be able to make the following assumption that:

The printout below refers to the weekly closing stock prices for Air Canada on 20 randomly selected weeks in 2000. Using a 5% level of significance, can you say that the average Air Canada stock price was less than $19.00?

The mean weight of newborn infants at a community hospital is said to be 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\alphaα = 0.05, what is the critical t value?

i. The probability of a Type I error is also referred to as alpha. ii. A Type I error is the probability of accepting a true null hypothesis. iii. A Type I error is the probability of rejecting a true null hypothesis.

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 25 and an unknown population standard deviation?

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two-tailed test at the 0.10 significance level is to be used. For what value of t will the null hypothesis be rejected?

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

What does z equal for an $\alpha$ = 0.01 and a lower level test?

i. If the critical values of the test statistic z are $\pm$ 1.96, they are the dividing points between the areas of rejection and non-rejection. ii. The probability of a Type I error is also referred to as alpha. iii. A Type I error is the probability of rejecting a true null hypothesis.

The mean weight of newborn infants at a community hospital is said to be 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 $\alpha$ = 0.05, what is the critical t value?