Exam 11: Statistical Inference Concerning Variance

The values of the distribution range from negative infinity to infinity.

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

The null hypothesis is rejected if the value of the test statistic exceeds .

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

Exhibit 11-3.The following are the competing hypotheses and the relevant summary statistics. Sample 1: n₁ = 10 Sample 2: n₂ = 9 Refer to Exhibit 11-3.Which of the following statements is true with regard to the assumptions for conducting the hypothesis test?

Exhibit 11-5.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 am to 10 am and evening 7 pm to 9 pm,for the analysis.Assume that wait times are normally distributed. Refer to Exhibit 11-5.Compute the value of the test statistic.

Find the value x for which: A) b. c. d.

(Use Excel)The following are the prices (in $1,000s)of 20 houses sold recently in Vancouver,Washington.A real estate agent believes that the standard deviation of house prices is less than 70 units,where each unit equals $1,000.Assume house prices are normally distributed. a.State the null and the alternative hypotheses for the test. B)Calculate the value of the test statistic. C)Use Excel's function (either CHISQ.DIST.RT or CHISQ.DIST)to calculate the p-value. D)At α = 0.10 what is the conclusion? Is the agent's claim supported by the data?

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

Exhibit 11-6.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.Here are some relevant summary statistics. Refer to Exhibit 4-6.At α = 0.10,is the analyst's claim supported by the data?

The following are the measures based on independently drawn samples from normally distributed populations: Sample 1: = 345,and n₁ = 25 Sample 2: = 276,and n₂ = 21 A)Construct a 90% interval estimate of the ratio of the population variances. B)Test if the ratio of the population variances differs from 1,using the computed confidence interval,at the 10% significance level.

Exhibit 11-6.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.Here are some relevant summary statistics. Refer to Exhibit 11-6.For the competing hypotheses: since ,approximate the p-value for the test.

For a 99% confidence level find with 6 degrees of freedom.

A professor analyzes the variance in scores between two sections that he teaches.The students of each section took the same test.The random samples drawn from the observations yield sample variances of = 203.15 and = 474.42 for samples of n₁ = 13 and n₂ = 16,respectively.Construct a 99% confidence interval for the ratio of the population variances.

Construct a 95% confidence interval for the ratios of two population variances.The random samples of n₁ = 9 and n₂ = 11 with sample variances of and ,respectively.Assume that the samples were drawn from a normal population.

Find the value of x for which = 0.05.

Use the p-value approach to conduct the following left-tailed hypothesis test at the 10% significance level.Assume that the two populations are normally distributed. Sample 1: = 15.7, = 0.77,and n₁ = 11 Sample 2: = 19.2, = 0.82,and n₂ = 13 [Hint: You may want to first convert the above left-tailed test into a right-tailed test by switching the two variances.]

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

A right-tailed test for the ratio of two population variances examines whether is greater than .

If s² is computed from a random sample of n observations drawn from an underlying normal population with a finite variance,then the variable is defined as ____.