Exam 11: Statistical Inference Concerning Variance

We can use the confidence intervals to implement _________ hypothesis tests regarding the population variance.

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?

The parameter of interest for inferences regarding the ratio of two population variances is their sum .

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.

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?

Which of the following Excel functions is used to determine the left-tailed value given any probability?

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.

If P( ≥ x)= 0.05,then the value of x is

Consider the hypotheses H₀:σ² ≤ 450,H_A:σ² > 450.Approximate the p-value based on the following sample information,where the sample is drawn from a normally distributed population. a.s² = 500;n = 15 b.s²= 600;n = 10 c.Which of the above sample information enables us to reject the null hypothesis at α = 0.10?

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 8a.m.to 10 a.m.and evening 7p.m.to 9p.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?

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 8a.m.to 10 a.m.and evening 7p.m.to 9p.m. ,for the analysis.Assume that wait times are normally distributed. Construct a 90% confidence interval and test if the ratio of the population variances differs from one at the 10% significance level.Which of the following outcomes supports the test?

Becky owns a diner and is concerned about sustaining the business.She wants to ascertain if the standard deviation of the profits for each week is greater than $250.The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916 Assume that profits are normally distributed.Using the critical value approach at α = 0.05,which of the following is the correct conclusion for Becky's concern?

Which of the following factors is used to conduct hypothesis tests regarding the population variance?

The supervisor of an automobile sales and service industry would like the variance of the number of automobiles serviced not to exceed five units-squared.He would recruit one more service executive if the variance exceeds this threshold.In a recent random sample of 14 services,he computed the sample standard deviation as 3.3.He believes that the automobile services are normally distributed. a.State the null and the alternative hypotheses to test if the threshold has been crossed. b.Use the critical value approach to conduct the test at α = 0.01. c.What should the supervisor do?

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.

The distribution is negatively skewed.

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?

The following table shows the heights (in inches)of individuals recorded recently for two families,the Williamses and the Thomases,in Chicago,Illinois: a.Construct a 95% interval estimate of the ratio of the population variances. b.Using the computed confidence interval,test if the ratio of the population variances differs from one at the 5% significance level.Explain.

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 At α = 0.10,is the analyst's claim supported by the data using the critical value approach?