Question 1

Which of the following has an F distribution?

Accepted Answer

A)  $\frac { ( n - 1 ) s } { \sigma }$ 
B)  $\frac { s _ { 1 } } { s _ { 2 } }$ 
C)  $\frac { ( n - 1 ) s _ { 1 } } { s _ { 2 } }$ 
D)  $\frac { s _ { 1 } ^ { 2 } } { s _ { 2 } ^ { 2 } } n$ 
A)  $\frac { ( n - 1 ) s } { \sigma }$ 
B)  $\frac { s _ { 1 } } { s _ { 2 } }$ 
C)  $\frac { ( n - 1 ) s _ { 1 } } { s _ { 2 } }$ 
D)  $\frac { s _ { 1 } ^ { 2 } } { s _ { 2 } ^ { 2 } } n$ A

Question 2

For an F distribution, the number of degrees of freedom for the numerator _____.

Accepted Answer

A)  must be larger than the number of degrees for the denominator 
B)  must be smaller than the number of degrees of freedom for the denominator 
C)  must be equal to the number of degrees of freedom for the denominator 
D)  can be larger, smaller, or equal to the number of degrees of freedom for the denominator 
A)  must be larger than the number of degrees for the denominator 
B)  must be smaller than the number of degrees of freedom for the denominator 
C)  must be equal to the number of degrees of freedom for the denominator 
D)  can be larger, smaller, or equal to the number of degrees of freedom for the denominator D

Question 3

A random sample of 20 observations showed a standard deviation of 8. At a 5% level of significance, test to see if the variance of the population is significantly less than 65.

Accepted Answer

​ $H _ { 0 } : \sigma ^ { 2 } = 65$
$H _ { \mathrm { a } } : \sigma ^ { 2 } < 65$
$x ^ { 2 } = 18.71 > 10.11$; do not reject $H _ { 0 }$, there is not sufficient evidence to conclude that the variance of the population is significantly less than 65 ​

Question 4

The critical value of F at 95% confidence when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is _____.

Accepted Answer

A)  2.45 
B)  2.94 
C)  2.37 
D)  2.10 
A)  2.45 
B)  2.94 
C)  2.37 
D)  2.10

Question 5

The State Highway Patrol (SHP) periodically samples vehicle speeds at Milepost 92 on Interstate 17. The SHP is concerned about the dispersion of speeds of vehicles sharing the same highway because significant difference in speed is a known cause of accidents. The speeds of a random sample of 16 vehicles are shown below.
​ $$\begin{array} { l l l l l l l l l } 
\text { Vehicle } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\text { Speed } & 69.6 & 73.5 & 74.1 & 64.4 & 66.3 & 68.7 & 69.0 & 65.2 \
\hline \text { Vehicle } & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \
\text { Speed } & 71.1 & 70.8 & 64.6 & 67.4 & 69.9 & 66.3 & 68.3 & 70.6
\end{array}$$ The SHP's policy is to position a patrol car at Milepost 92 on Interstate 17 if the vehicle speed variance at that location is believed to be greater than 6 mph. Conduct a hypothesis test (with a = .10) to determine whether the speed variance for all vehicles passing Milepost 92 exceeds 6 mph.

Accepted Answer

H₀: σ² ≤ 6.0 and H_a: σ²

Question 6

The sampling distribution of the ratio of two independent sample variances taken from normal populations with equal variances is a(n) _____ distribution.

Accepted Answer

A)  F 
B)  χ2 
C)  t 
D)  normal 
A)  F 
B)  χ2 
C)  t 
D)  normal

Question 7

Which of the following has a χ2 distribution?

Accepted Answer

A)  (n - 1)σ2/s2 
B)  (n - 2)σ2/s2 
C)  (n - 1)s/σ 
D)  (n - 1)s2/σ2 
A)  (n - 1)σ2/s2 
B)  (n - 2)σ2/s2 
C)  (n - 1)s/σ 
D)  (n - 1)s2/σ2

Question 8

A company claims that the standard deviation in its delivery time is less than 5 days. A sample of 27 past customers is taken. The average delivery time in the sample was 14 days with a standard deviation of 4.5 days. At a 5% level of significance, test the company's claim.

Accepted Answer

The answer of A company claims that the standard deviation...

Question 9

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 ≥ 49 
C)  s  49 
A)  σ 2 ≥ 49 
C)  s  49

Question 10

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is _____.

Accepted Answer

A)  2.48 
B)  2.58 
C)  3.63 
D)  2.96 
A)  2.48 
B)  2.58 
C)  3.63 
D)  2.96

Question 11

A sample of 10 earnings per share estimates is shown below. $$\begin{array} { l l l l l } 
2.92 & 4.60 & 4.20 & 3.10 & 3.66 \
7.22 & 2.54 & 1.45 & 2.88 & 3.64
\end{array}$$ Use Excel to estimate the variance with a 95% level of confidence.

Accepted Answer

The answer of A sample of 10 earnings per share...

Question 12

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is _____.

Accepted Answer

A)  H0: σ2 0: s2 ≥ 1.44 
C)  H0: σ ≤ 1.20 
D)  H0: σ2 ≥ 1.44 
A)  H0: σ2 0: s2 ≥ 1.44 
C)  H0: σ ≤ 1.20 
D)  H0: σ2 ≥ 1.44

Question 13

A manufacturing company is considering changing suppliers of a particular raw material. The standard deviation of days until delivery for the current supplier is 3. A sample of five delivery times is taken from the new supplier. The data follow:
2
2
1
5
3
The manufacturing company will use the new supplier if the variance in delivery time is less than that of the current supplier. Use Excel to determine whether the company should use the new supplier. Use a 10% level of significance.

Accepted Answer

@#IMG-DLM& Reject H₀, there i

Question 14

We are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 16 days of sales at each store indicated the following: $\begin{array} { l l } 
\text { Store A } & \text { Store B } \
n _ { 1 } = 16 & n _ { 2 } = 16 \
s _ { 1 } = \$ 125 & s _ { 2 } = \$ 105
\end{array}$ Are the variances of the populations (from which these samples came) equal?
Use α = .05.

Accepted Answer

F = 1.42; do not reject H₀, the

Question 15

Student advisors are interested in determining if the variances of the grades of day students and night students are the same. The following samples are drawn: $$\begin{array} { l l } 
\text { Day } & \text { Night } \
n _ { 1 } = 25 & n _ { 2 } = 31 \
s _ { 1 } = 9.8 & s _ { 2 } = 14.7
\end{array}$$ Test the equality of the variances of the populations at 95% confidence.

Accepted Answer

Since F = 2.25 > 2.21, reject

Question 16

A company has claimed that the standard deviation of the monthly incomes of its employees is less than or equal to $120. To test its claim, a random sample of 15 employees of the company was taken, and it was determined that the standard deviation of their incomes was $135. At a 5% level of significance, test the company's claim.

Accepted Answer

@#IMG-DLM& Do not reject H_0, t

Question 17

The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of .2. The p-value for the test is _____.

Accepted Answer

A)  between .025 and .05 
B)  between .05 and .01 
C)  .05 
D)  .025 
A)  between .025 and .05 
B)  between .05 and .01 
C)  .05 
D)  .025

Question 18

In Excel, which of the following functions is used to conduct a hypothesis test for comparing two population variances?

Accepted Answer

A)  CHISQ.DIST 
B)  F-Test 
C)  CHI.INV 
D)  None of the answers is correct. 
A)  CHISQ.DIST 
B)  F-Test 
C)  CHI.INV 
D)  None of the answers is correct.

Question 19

The standard deviation of the ages of a sample of 16 executives from the northern states was 8.2 years, while the standard deviation of the ages of a sample of 25 executives from the southern states was 12.8 years. At α = .1, test to see if there is any difference in the standard deviations of the ages of all the northern and southern executives.

Accepted Answer

Since F = 2.44 > 2.29, reject

Question 20

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all its new automobiles is _____.

Accepted Answer

A)  8.58 to 39.79 
B)  4 to 16 
C)  4 to 15 
D)  1.64 to 1.96 
A)  8.58 to 39.79 
B)  4 to 16 
C)  4 to 15 
D)  1.64 to 1.96

Which of the following has an F distribution?

For an F distribution, the number of degrees of freedom for the numerator _____.

A random sample of 20 observations showed a standard deviation of 8. At a 5% level of significance, test to see if the variance of the population is significantly less than 65.

The critical value of F at 95% confidence when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is _____.

The sampling distribution of the ratio of two independent sample variances taken from normal populations with equal variances is a(n) _____ distribution.

Which of the following has a χ² distribution?

A company claims that the standard deviation in its delivery time is less than 5 days. A sample of 27 past customers is taken. The average delivery time in the sample was 14 days with a standard deviation of 4.5 days. At a 5% level of significance, test the company's claim.

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

The value of F_.05 with 8 numerator and 19 denominator degrees of freedom is _____.

A sample of 10 earnings per share estimates is shown below. 2.92 4.60 4.20 3.10 3.66 7.22 2.54 1.45 2.88 3.64 Use Excel to estimate the variance with a 95% level of confidence.

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is _____.

Student advisors are interested in determining if the variances of the grades of day students and night students are the same. The following samples are drawn: Day Night =25 =31 =9.8 =14.7 Test the equality of the variances of the populations at 95% confidence.

The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of .2. The p-value for the test is _____.

In Excel, which of the following functions is used to conduct a hypothesis test for comparing two population variances?

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all its new automobiles is _____.

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

Tests of Goodness of Fit, Independence, and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

Exam 11: Inferences About Population Variances

Which of the following has an F distribution?

For an F distribution, the number of degrees of freedom for the numerator _____.

A random sample of 20 observations showed a standard deviation of 8. At a 5% level of significance, test to see if the variance of the population is significantly less than 65.

The critical value of F at 95% confidence when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is _____.

The sampling distribution of the ratio of two independent sample variances taken from normal populations with equal variances is a(n) _____ distribution.

Which of the following has a χ2 distribution?

A company claims that the standard deviation in its delivery time is less than 5 days. A sample of 27 past customers is taken. The average delivery time in the sample was 14 days with a standard deviation of 4.5 days. At a 5% level of significance, test the company's claim.

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

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is _____.

A sample of 10 earnings per share estimates is shown below. 2.92 4.60 4.20 3.10 3.66 7.22 2.54 1.45 2.88 3.64 Use Excel to estimate the variance with a 95% level of confidence.

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is _____.

Student advisors are interested in determining if the variances of the grades of day students and night students are the same. The following samples are drawn: Day Night =25 =31 =9.8 =14.7 Test the equality of the variances of the populations at 95% confidence.

The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of .2. The p-value for the test is _____.

In Excel, which of the following functions is used to conduct a hypothesis test for comparing two population variances?

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all its new automobiles is _____.

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

Tests of Goodness of Fit, Independence, and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

Which of the following has a χ² distribution?

The value of F_.05 with 8 numerator and 19 denominator degrees of freedom is _____.