Exam 11: Statistical Inference Concerning Variance

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.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?

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 in order 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?

Construct a 95% interval estimate of the ratio of the population variances using the following results from two independently drawn samples from normally distributed populations. Sample 1: = 102, = 22.48,and n₁ = 16 Sample 2: = 98, = 18.10,and n₂ = 13

Statistical inferences pertaining to σ² are based on which of the following distributions?

Use the F table to approximate the following probabilities: A) b. c. d.

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.

A supermarket has just added a new cash register to reduce the waiting times of the customers during weekends.Since a new cash register is added,the customers expect that their waiting time will be less than the waiting time before the cash register was added.Suppose the sample variance of the waiting times for 25 customers before adding the new cash register is = 4.8 minutes,while the sample variance of the waiting times for 25 customers after adding the cash register is = 2.2 minutes.The manager of the supermarket believes that the waiting times are normally distributed and that the two samples are drawn independently. A)Develop the hypotheses to test whether the ratio of two population variances is less than 1. B)Calculate the appropriate test statistic. C)Using the p-value approach,determine the decision rule at the 5% significance level. D)What is the conclusion? Given that all other criteria are satisfied,should the supermarket continue with the new cash register?

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.At the 10% significance level,what is the conclusion?

The supervisor of an automobile sales and service industry would like the variance of the number of automobiles serviced not to exceed 5 units-squared.He would recruit one more service executive if the variance exceeds this threshold.In a recent random sample of 14 services,he computes 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?

Consider the following hypotheses: 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.

Which of the following is the formula for a confidence interval for the ratio of the population variances ?

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

If independent samples of size n₁ and n₂ are drawn from normal populations with equal variances,then the value of the F_(df1,df2) statistic is calculated as ____.

The value of the test statistic to test the ratio of two population variances is .

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 population variance is one of the most widely used quantitative measures of risk in investments.