Question 1

The symbol used for the variance of the population is

Accepted Answer

A)  σ. 
B)  σ2. 
C)  s. 
D)  s2. 
A)  σ. 
B)  σ2. 
C)  s. 
D)  s2. B

Question 2

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are​

Accepted Answer

A)  11.808 and 49.645. 
B)  ​14.573 and 43.195. 
C)  ​16.151 and 40.113. 
D)  ​15.308 and 44.461. 
A)  11.808 and 49.645. 
B)  ​14.573 and 43.195. 
C)  ​16.151 and 40.113. 
D)  ​15.308 and 44.461. B

Question 3

A sample of 31 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

Accepted Answer

A)  20. 
B)  21. 
C)  30. 
D)  7.5. 
A)  20. 
B)  21. 
C)  30. 
D)  7.5. C

Question 4

?Which of the following rejection rules is proper?

Accepted Answer

A)  ?Reject H0 if p-value ? F?. 
B)  ?Reject H0 if F ? F?/2. 
C)  ?Reject H0 if p-value ? ?/2. 
D)  ?Reject H0 if F ? F?. 
A)  ?Reject H0 if p-value ? F?. 
B)  ?Reject H0 if F ? F?/2. 
C)  ?Reject H0 if p-value ? ?/2. 
D)  ?Reject H0 if F ? F?.

Question 5

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B.   ​ The test statistic for this problem equals

Accepted Answer

A)  .4132. 
B)  1.1. 
C)  2.42. 
D)  2. 
A)  .4132. 
B)  1.1. 
C)  2.42. 
D)  2.

Question 6

​Consider the following hypothesis problem.   ​ ​The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

Accepted Answer

A)  22.362. 
B)  ​23.685. 
C)  ​5.009 and 24.736. 
D)  ​5.629 and 26.119. 
A)  22.362. 
B)  ​23.685. 
C)  ​5.009 and 24.736. 
D)  ​5.629 and 26.119.

Question 7

A sample of 60 items from population 1 has a sample variance of 12 while a sample of 50 items from population 2 has a sample variance of 15. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of

Accepted Answer

A)  .8. 
B)  1.56. 
C)  1.5. 
D)  1.25. 
A)  .8. 
B)  1.56. 
C)  1.5. 
D)  1.25.

Question 8

Consider the following hypothesis problem.   ​ The test statistic has a value of

Accepted Answer

A)  20.91. 
B)  24.20. 
C)  24.00. 
D)  20.00. 
A)  20.91. 
B)  24.20. 
C)  24.00. 
D)  20.00.

Question 9

​Consider the following hypothesis problem.   ​ At the 5% level of significance, the null hypothesis

Accepted Answer

A)  ​should be rejected. 
B)  ​should not be rejected. 
C)  ​should be revised. 
D)  should not be tested. 
A)  ​should be rejected. 
B)  ​should not be rejected. 
C)  ​should be revised. 
D)  should not be tested.

Question 10

​Consider the following hypothesis problem.   ​ At the 5% level of significance, the null hypothesis

Accepted Answer

A)  should be rejected​. 
B)  ​should not be rejected​. 
C)  ​should be revised. 
D)  should not be tested. 
A)  should be rejected​. 
B)  ​should not be rejected​. 
C)  ​should be revised. 
D)  should not be tested.

Question 11

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

Accepted Answer

A)  chi-square distribution. 
B)  normal distribution. 
C)  F distribution. 
D)  t distribution. 
A)  chi-square distribution. 
B)  normal distribution. 
C)  F distribution. 
D)  t distribution.

Question 12

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

Accepted Answer

A)  σ 2 ≥ 7. 
C)  σ 2 ≥ 49. 
A)  σ 2 ≥ 7. 
C)  σ 2 ≥ 49.

Question 13

The sampling distribution of the quantity (n - 1)s2/σ2 is the

Accepted Answer

A)  chi-square distribution. 
B)  normal distribution. 
C)  F distribution. 
D)  t distribution. 
A)  chi-square distribution. 
B)  normal distribution. 
C)  F distribution. 
D)  t distribution.

Question 14

Consider the following hypothesis problem. ​   ​
The p-value is

Accepted Answer

A)  less than .025. 
B)  between .025 and .05. 
C)  between .05 and .10. 
D)  greater than .10. 
A)  less than .025. 
B)  between .025 and .05. 
C)  between .05 and .10. 
D)  greater than .10.

Question 15

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is at most .05. The null hypothesis in a test to confirm the claim would be written as

Accepted Answer

A)  H0: σ2 ≥ .05. 
B)  H0: s2 ≥ .05. 
C)  H0: s2 ≤ .05. 
D)  H0: σ2 ≤ .05. 
A)  H0: σ2 ≥ .05. 
B)  H0: s2 ≥ .05. 
C)  H0: s2 ≤ .05. 
D)  H0: σ2 ≤ .05.

Question 16

Consider the following hypothesis problem. ​   ​
If the test is to be performed at the 5% level, the critical value(s) from the chi-square distribution table is(are)

Accepted Answer

A)  10.982 and 36.781. 
B)  12.338 and 33.924. 
C)  12.338. 
D)  33.924. 
A)  10.982 and 36.781. 
B)  12.338 and 33.924. 
C)  12.338. 
D)  33.924.

Question 17

The standard deviation of the daily temperatures in Honolulu last year was 4 degrees Fahrenheit. A random sample of 25 days resulted in a standard deviation of 5.8 degrees Fahrenheit. Has there been a significant increase in the variance of the temperatures? Use α = .05.

Accepted Answer

Since χ² = 50.46 > 36.415 (p-va

Question 18

Which of the following has an F distribution?

Accepted Answer

A)  (n - 1)s/σ. 
B)  s1/s2. 
C)  (n - 1)s1/s2. 
D)    . 
A)  (n - 1)s/σ. 
B)  s1/s2. 
C)  (n - 1)s1/s2. 
D)    .

Question 19

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The null hypothesis is

Accepted Answer

A)  s2 > .003. 
B)  s2 ≤ .003. 
C)  σ2 > .003. 
D)  σ2 ≤ .003. 
A)  s2 > .003. 
B)  s2 ≤ .003. 
C)  σ2 > .003. 
D)  σ2 ≤ .003.

Question 20

Which of the following has a chi-square distribution?

Accepted Answer

A)  (n - 1)s2/σ2. 
B)  (n - 1)σ/s. 
C)  (n - 1.0)s/σ. 
D)  (n - 1.0)s2/σ2. 
A)  (n - 1)s2/σ2. 
B)  (n - 1)σ/s. 
C)  (n - 1.0)s/σ. 
D)  (n - 1.0)s2/σ2.

Exam 11: Inferences About Population Variances

The symbol used for the variance of the population is

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are​

A sample of 31 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

?Which of the following rejection rules is proper?

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. ​ The test statistic for this problem equals

​Consider the following hypothesis problem. ​ ​The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

A sample of 60 items from population 1 has a sample variance of 12 while a sample of 50 items from population 2 has a sample variance of 15. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of

Consider the following hypothesis problem. ​ The test statistic has a value of

​Consider the following hypothesis problem. ​ At the 5% level of significance, the null hypothesis

​Consider the following hypothesis problem. ​ At the 5% level of significance, the null hypothesis

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

The sampling distribution of the quantity (n - 1)s2/σ2 is the

Consider the following hypothesis problem. ​ ​ The p-value is

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is at most .05. The null hypothesis in a test to confirm the claim would be written as

Consider the following hypothesis problem. ​ ​ If the test is to be performed at the 5% level, the critical value(s) from the chi-square distribution table is(are)

The standard deviation of the daily temperatures in Honolulu last year was 4 degrees Fahrenheit. A random sample of 25 days resulted in a standard deviation of 5.8 degrees Fahrenheit. Has there been a significant increase in the variance of the temperatures? Use α = .05.

Which of the following has an F distribution?

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The null hypothesis is

Which of the following has a chi-square distribution?

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Comparing Multiple Proportions, Tests of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Decision Analysis

Index Numbers

Statistical Methods for Quality Control

Sample Survey

Filters

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are

A sample of 31 observations yielded a sample variance of 16. If we want to test H₀: σ² = 16, the test statistic is

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. The test statistic for this problem equals

Consider the following hypothesis problem. The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

Consider the following hypothesis problem. The test statistic has a value of

Consider the following hypothesis problem. At the 5% level of significance, the null hypothesis

Consider the following hypothesis problem. At the 5% level of significance, the null hypothesis

The sampling distribution of the quantity (n - 1)s²/σ² is the

Consider the following hypothesis problem. The p-value is

Consider the following hypothesis problem. If the test is to be performed at the 5% level, the critical value(s) from the chi-square distribution table is(are)