Exam 11: Statistical Inference Concerning Variance

Which of the following R functions is used to obtain a right-tail probability for a value x of the distribution?

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(are) the critical value(s) at α = 0.05?

For a sample of 10 observations drawn from a normally distributed population, we obtain the sample mean and the sample variance as 50 and 75, respectively. We want to determine whether the population variance is greater than 70. The test statistic is

Two students, Mary and Joanna, are in a statistics class working hard on the consistency of their performance in the weekly class tests. In particular, they are hoping to bring down the variance of their test scores. Their professor believes that the students are not equally consistent in their tests. Over a 12-week period, the test scores of these two students are shown below. Assume that the two samples are drawn independently from normally distributed populations. a. Develop the hypotheses to test whether the two students differ in consistency. B) Use the critical value approach to test the professor's claim at α = 0.05.

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 95% confidence interval for the ratio of the population variances?

The relevant value in the ________ tail of the distribution is .

The ________ is the probability distribution of the sum of several independent squared standard normal random variables.

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. A 90% confidence interval is found to be [1.19, 7.36], where the morning is the first group and the evening is the second group. Which of the following is the correct conclusion?

The monthly adjusted (for dividends and splits) closing stock prices (rounded to the nearest dollar) for Gladstone Commercial Corp. and Kimco Realty Corp. for the last six months of 2010 are reported in the table below a. State the null and the alternative hypotheses to determine if the variance of price differs for the two firms. B) What assumption regarding the population is necessary to implement this step? C) Use Excel's F.TEST function to calculate the p-value. D) At α = 0.05 what is your conclusion?

The following table shows the annual returns (in percent) for the Fidelity Utilities fund from 2006 through 2010. a. Calculate the point estimate of σ². B) Construct a 95% confidence interval of σ².

Statistical inference about σ² is based on which of the following distributions?

Consider the following hypotheses: H₀: σ² = 169, H_A: σ² ≠ 169 A sample variance of 98 is obtained from a random sample of 10 observations drawn from a normally distributed population. At 1% significance level, conduct a test for the population variance using the critical value approach.

The following are the competing hypotheses and the relevant summary statistics: Η₀: / ≤ 1, Η_A: / > 1. Which of the following is the critical value at the 5% significance level?

The administrator of a college is concerned about the students using cell phones for texting during the class hours. She randomly selects 25 students to check if the variance of the number of students in the college using cell phones during the class hours is less than 12. She arrives at a sample variance of 7. She assumes the distribution to be normal. A) State the appropriate null and alternative hypotheses for the test. B) Compute the value of the test statistic. C) Use the critical value approach to test the administrator's concern at α = 0.10. D) Repeat the test at α = 0.01.

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. Which of the following is the correct p-value?

A right-tailed test for the ratio of two population variances Η₀: / ≤ 1 examines whether is greater than .

Use the p-value approach to conduct the following left-tailed hypothesis test at the 10% significance level. Use the following results from two independently drawn samples from normally distributed populations: Η₀: / ≥ 1, Η_A: / < 1.

The Excel's function ________ returns the p-value for a right-tailed test for the ratio of two population variances.

How does the width of the interval respond to the changes in the confidence level?

Use the R function ________ to obtain a p-value for a test about the ratio of two population variances.