Question 1

Which of the following hypotheses is a right-tail test about the population variance?

Accepted Answer

A)  Η0: σ2 =   , ΗA: σ2 ≠   
B)  Η0: σ2 ≤   , ΗA: σ2 >   
C)  Η0: σ2 >   , ΗA: σ2 0: σ2 ≥   , ΗA: σ2 >   
A)  Η0: σ2 =   , ΗA: σ2 ≠   
B)  Η0: σ2 ≤   , ΗA: σ2 >   
C)  Η0: σ2 >   , ΗA: σ2 0: σ2 ≥   , ΗA: σ2 >

Question 2

Consider the expected returns (in percent) from the two investment options. Beth claims that the variances of the returns for the two investments differ. Use the following data to arrive at the results.   Test Beth's claim at the 5% significance level. Which of the following is the correct conclusion?

Accepted Answer

A) p-value = 0.7127 > α = 0.05; Beth's claim is correct. B) p-value = 0.7127 > α = 0.05; Beth's claim is wrong. C) p-value = 0.7127 < α = 0.05; Beth's claim is wrong. D) p-value = 0.7127 < α = 0.05; Beth's claim is correct. A) p-value = 0.7127 > α = 0.05; Beth's claim is correct. B) p-value = 0.7127 > α = 0.05; Beth's claim is wrong. C) p-value = 0.7127 < α = 0.05; Beth's claim is wrong. D) p-value = 0.7127 < α = 0.05; Beth's claim is correct.

Question 3

Which of the following is used to conduct a hypothesis test about the population variance?

Accepted Answer

A)  Sample mean 
B)  Population mean 
C)  Sample proportion 
D)  Sample variance 
A)  Sample mean 
B)  Population mean 
C)  Sample proportion 
D)  Sample variance

Question 4

The value of the test statistic for the hypothesis test of the population variance, σ2 is computed as   =   .

Accepted Answer

A) True 
 B)False

Question 5

The following are the competing hypotheses and the relevant summary statistics: Η0:   /   ≤ 1, ΗA:   /   > 1.   The p-value associated with the value of the test statistic is 0.3692. At the 5% significance level, which of the following conclusions is correct?

Accepted Answer

A)  We reject the null hypothesis and conclude the first variance is larger than the second. 
B)  We do not reject the null hypothesis and conclude the first variance is larger than the second. 
C)  We reject the null hypothesis and cannot conclude the first variance is larger than the second. 
D)  We do not reject the null hypothesis and cannot conclude the first variance is larger than the second. 
A)  We reject the null hypothesis and conclude the first variance is larger than the second. 
B)  We do not reject the null hypothesis and conclude the first variance is larger than the second. 
C)  We reject the null hypothesis and cannot conclude the first variance is larger than the second. 
D)  We do not reject the null hypothesis and cannot conclude the first variance is larger than the second.

Question 6

A researcher compares the returns for two mutual funds, Smith, Inc. and Campbell, Inc. to determine which of the two has a higher risk rate. She assumes that the returns are normally distributed. Implement the critical value approach at a significance level of 10%. The sample descriptive measures are given below.

Accepted Answer

We reject the null hypothesis

Question 7

Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers'; tastes and current fads. Consider the following growth rates (in percent) for two companies in this industry, Hasbro and Mattel.   Which of the following is the correct conclusion?

Accepted Answer

A)  Do not reject Η0. We can conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. 
B)  Reject Η0. We can conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. 
C)  Do not reject Η0. We cannot conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. 
D)  Reject Η0. We cannot conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. 
A)  Do not reject Η0. We can conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. 
B)  Reject Η0. We can conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. 
C)  Do not reject Η0. We cannot conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. 
D)  Reject Η0. We cannot conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel.

Question 8

The following table shows the annual returns (in percent) for Fidelity's Technology and Communications funds for the years 2006 through 2010.   Use the critical value approach to test if the population variances differ at the 10% significance level.

Accepted Answer

The competing hypotheses are Η

Question 9

Use the F table to approximate these probabilities.
A) P(F(8,12) ≥ 2.85)
B) P(F(8,12) (5,5) ≥ 7.15)
D) P(F(5,5) < 0.09)

Accepted Answer

a. 0.05
b.

Question 10

If a sample of size n is taken from a normal population with a finite variance, then the statistic   =   follows the   distribution with degrees of freedom.

Accepted Answer

A)  (n + 1)(n − 1). 
B)  n + 1. 
C)  n − 1. 
D)  n. 
A)  (n + 1)(n − 1). 
B)  n + 1. 
C)  n − 1. 
D)  n.

Question 11

The following are the measures based on independently drawn samples from normally distributed populations.   a. Construct a 90% interval estimate of the ratio of the population variances.
B) Test if the ratio of the population variances differs from Sample 1, using the computed confidence interval, at the 10% significance level.

Accepted Answer

a. [0.60, 2.54]
b. R

Question 12

The   distribution is negatively skewed.

Accepted Answer

A) True 
 B)False

Question 13

The result of placing a larger sample variance in the numerator of the   test statistic allows us to

Accepted Answer

A)  focus only on the right tail of the distribution. 
B)  arrive at a more accurate   statistic value. 
C)  focus only on the left tail of the distribution. 
D)  determine if the distribution is symmetric. 
A)  focus only on the right tail of the distribution. 
B)  arrive at a more accurate   statistic value. 
C)  focus only on the left tail of the distribution. 
D)  determine if the distribution is symmetric.

Question 14

Consider the expected returns (in percent) from two investment options. Beth wants to determine if investment 1 has a lower variance. Use the following summary statistics.   Which of the following are the competing hypotheses for this test?

Accepted Answer

A) Η0: / ≤ 1, ΗA: / > 1 B) Η0: / ≤ 1, ΗA: / > 1 C) Η0: / = 1, ΗA: / ≠ 1 D) Η0: / ≥ 1, ΗA: / < 1 A) Η0: / ≤ 1, ΗA: / > 1 B) Η0: / ≤ 1, ΗA: / > 1 C) Η0: / = 1, ΗA: / ≠ 1 D) Η0: / ≥ 1, ΗA: / < 1

Question 15

The null hypothesis H0: σ2 ≤   is rejected if the value of the test statistic exceeds   .

Accepted Answer

A) True 
 B)False

Question 16

The sales price (in $1,000) of three-bedroom apartments in two cities-Houston, Texas, and Orlando, Florida-are given in the following table. Houston is known to have lower house prices than Orlando; however, it is not clear if it also has lesser variability in its prices.   a. State the null and the alternative hypotheses to determine if the variance of house price in Houston is less than that in Orlando.
B) What assumption regarding the population is necessary to implement this step?
C) Test the hypothesis at α = 0.05. What is your conclusion?

Accepted Answer

a. Η₀: @#IMG-DLM& / @#IMG-DLM& ≥ 1, Η_A: @#IMG-DLM& / @#IMG-DLM& < 1 b. House price

Question 17

A financial analyst examines the performance of two mutual funds and claims that the variances of the annual returns for the bond funds differ. To support his claim, he collects data on the annual returns (in percent) for the years 2001 through 2010. The analyst assumes that the annual returns for the two emerging market bond funds are normally distributed. Use the following summary statistics.   The competing hypotheses are Η0:   /   = 1, ΗA:   /   ≠ 1. At α = 0.10, is the analyst's claim supported by the data using the critical value approach?

Accepted Answer

A)  No, because the value of the test statistic is less than the critical F value. 
B)  Yes, because the value of the test statistic is less than the critical F value. 
C)  Yes, because the value of the test statistic is greater than the critical F value. 
D)  No, because the value of the test statistic is greater than the critical F value. 
A)  No, because the value of the test statistic is less than the critical F value. 
B)  Yes, because the value of the test statistic is less than the critical F value. 
C)  Yes, because the value of the test statistic is greater than the critical F value. 
D)  No, because the value of the test statistic is greater than the critical F value.

Question 18

The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared. He would like to add an additional billing counter if the variance exceeds the cut-off. He checks the recent sample data. For a random sample of 24 customer waiting times, he arrives at a sample variance of 3.8 minutes-squared. The manager assumes the waiting times to be normally distributed. At α = 0.05, which of the following is the critical value   ?

Accepted Answer

A)  13.091 
B)  32.007 
C)  35.172 
D)  38.076 
A)  13.091 
B)  32.007 
C)  35.172 
D)  38.076

Question 19

Find the value x for which
A) P(   ≥ x) = 0.10.
B) P(   < x) = 0.10.
C) P(   ≥ x) = 0.05.
D) P(   < x) = 0.05.

Accepted Answer

a. 24.769

Question 20

Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two peak hours, morning 8 a.m. to 10 a.m., and evening 7 p.m. to 9 p.m., for the analysis. Assume that wait times are normally distributed.   Which of the following is the correct hypotheses to determine if the variance of wait time during morning peak hours (population 1) differs from that during the evening peak hours (population 2)?

Accepted Answer

A) Η0: / ≤ 1, ΗA: / > 1 B) Η0: / ≤ 1, ΗA: / > 1 C) Η0: / = 1, ΗA: / ≠ 1 D) Η0: / ≥ 1, ΗA: / < 1 A) Η0: / ≤ 1, ΗA: / > 1 B) Η0: / ≤ 1, ΗA: / > 1 C) Η0: / = 1, ΗA: / ≠ 1 D) Η0: / ≥ 1, ΗA: / < 1

Which of the following hypotheses is a right-tail test about the population variance?

Consider the expected returns (in percent) from the two investment options. Beth claims that the variances of the returns for the two investments differ. Use the following data to arrive at the results. Test Beth's claim at the 5% significance level. Which of the following is the correct conclusion?

Which of the following is used to conduct a hypothesis test about the population variance?

The value of the test statistic for the hypothesis test of the population variance, σ² is computed as = .

The following are the competing hypotheses and the relevant summary statistics: Η₀: / ≤ 1, Η_A: / > 1. The p-value associated with the value of the test statistic is 0.3692. At the 5% significance level, which of the following conclusions is correct?

Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers'; tastes and current fads. Consider the following growth rates (in percent) for two companies in this industry, Hasbro and Mattel. Which of the following is the correct conclusion?

The following table shows the annual returns (in percent) for Fidelity's Technology and Communications funds for the years 2006 through 2010. Use the critical value approach to test if the population variances differ at the 10% significance level.

Use the F table to approximate these probabilities. A) P(F_(8,12) ≥ 2.85) B) P(F_(8,12) < 0.4) C) P(F_(5,5) ≥ 7.15) D) P(F_(5,5) < 0.09)

If a sample of size n is taken from a normal population with a finite variance, then the statistic = follows the distribution with degrees of freedom.

The distribution is negatively skewed.

The result of placing a larger sample variance in the numerator of the test statistic allows us to

Consider the expected returns (in percent) from two investment options. Beth wants to determine if investment 1 has a lower variance. Use the following summary statistics. Which of the following are the competing hypotheses for this test?

The null hypothesis H₀: σ² ≤ is rejected if the value of the test statistic exceeds .

Find the value x for which A) P( ≥ x) = 0.10. B) P( < x) = 0.10. C) P( ≥ x) = 0.05. D) P( < x) = 0.05.

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

Exam 11: Statistical Inference Concerning Variance

Which of the following hypotheses is a right-tail test about the population variance?

Which of the following is used to conduct a hypothesis test about the population variance?

The value of the test statistic for the hypothesis test of the population variance, σ2 is computed as = .

The following are the competing hypotheses and the relevant summary statistics: Η0: / ≤ 1, ΗA: / > 1. The p-value associated with the value of the test statistic is 0.3692. At the 5% significance level, which of the following conclusions is correct?

Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers'; tastes and current fads. Consider the following growth rates (in percent) for two companies in this industry, Hasbro and Mattel. Which of the following is the correct conclusion?

The following table shows the annual returns (in percent) for Fidelity's Technology and Communications funds for the years 2006 through 2010. Use the critical value approach to test if the population variances differ at the 10% significance level.

Use the F table to approximate these probabilities. A) P(F(8,12) ≥ 2.85) B) P(F(8,12) < 0.4) C) P(F(5,5) ≥ 7.15) D) P(F(5,5) < 0.09)

If a sample of size n is taken from a normal population with a finite variance, then the statistic = follows the distribution with degrees of freedom.

The distribution is negatively skewed.

The result of placing a larger sample variance in the numerator of the test statistic allows us to

Consider the expected returns (in percent) from two investment options. Beth wants to determine if investment 1 has a lower variance. Use the following summary statistics. Which of the following are the competing hypotheses for this test?

The null hypothesis H0: σ2 ≤ is rejected if the value of the test statistic exceeds .

Find the value x for which A) P( ≥ x) = 0.10. B) P( < x) = 0.10. C) P( ≥ x) = 0.05. D) P( < x) = 0.05.

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

The value of the test statistic for the hypothesis test of the population variance, σ² is computed as = .

The following are the competing hypotheses and the relevant summary statistics: Η₀: / ≤ 1, Η_A: / > 1. The p-value associated with the value of the test statistic is 0.3692. At the 5% significance level, which of the following conclusions is correct?

Use the F table to approximate these probabilities. A) P(F_(8,12) ≥ 2.85) B) P(F_(8,12) < 0.4) C) P(F_(5,5) ≥ 7.15) D) P(F_(5,5) < 0.09)

The null hypothesis H₀: σ² ≤ is rejected if the value of the test statistic exceeds .