Exam 10: Estimation and Hypothesis Testing for Two Population Parameters

In order to test the difference in populations means,samples were collected for two independent populations where the variances are assumed equal and the population normally distributed.The following data resulted: The value of the pooled standard deviation is 15.66.

Recently the managers for a large retail department store stated that a study has revealed that female shoppers spend on average 23.5 minutes longer in the store per visit than do male shoppers.Based on this information,the managers can be confident that female shoppers,as a population,do spend longer times in the store than do males shoppers,as a population.

There have been complaints recently from homeowners in the north end claiming that their homes have been assessed at values that are too high compare with other parts of town.They say that the mean increase from last year to this year has been higher in their part of town than elsewhere.To test this,the assessor's office staff plans to select a random sample of north end properties (group 1)and a random sample of properties from other areas within the city (group 2)and perform a hypothesis test.The following sample information is available: Assuming that the null hypothesis will be tested using an alpha level equal to 0.05,what is the value of the test statistic?

The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers.It wishes to estimate this difference using a 95 percent confidence level.If the sample size is n = 10 from each population,the samples are independent,and sample standard deviations are used,and the variances are assumed equal,then the critical value will be t = 2.1009.

Suppose that two population proportions are being compared to test whether there is any difference between them.Assume that the test statistic has been calculated to be z = 2.21.Find the p-value for this situation.

When estimating the difference between two population means,when should the normal distribution be used and when should the t-distribution be used?

An Internet service provider is interested in estimating the proportion of homes in a particular community that have computers but do not already have Internet access.To do this,the company has selected a random sample of n = 200 homes and made calls.A total of 188 homes responded to the survey question with 38 saying that they had a computer with no Internet access.The 95 percent confidence interval estimate for the true population proportion is approximately 0.1447 - 0.2595.

There are a number of highly touted search engines for finding things of interest on the Internet.Recently,a consumer rating system ranked two search engines ahead of the others.Now,a computer user's magazine wishes to make the final determination regarding which one is actually better at finding particular information.To do this,each search engine was used in an attempt to locate specific information using specified keywords.Both search engines were subjected to 100 queries.Search engine 1 successfully located the information 88 times and search engine 2 located the information 80 times.Using a significance level equal to 0.05,which of the following is true?

A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates who go on to graduate school within five years after graduation and the proportion of non-business school graduates who attend graduate school.A random sample of 400 business school graduates showed that 75 had gone to graduate school while in a random sample of 500 non-business graduates,137 had gone on to graduate school.Based on a 95 percent confidence level,what is the upper limit of the confidence interval estimate?

An advertising company has developed a new ad for one of the national car manufacturing companies.The ad agency is interested in testing whether the proportion of favorable response to the ad is the same between male adults versus female adults.It plans on conducting the test using an alpha level equal to 0.05.A sample of 100 adults of each gender will be used in the study.Each person will be asked to view the ad and indicate whether they find the ad to be "pleasing" or not.The samples resulted in 57 males that liked the ad and 47 females that liked the ad.Based on this information,what is the value of the test statistic?

An accounting firm has been hired by a large computer company to determine whether the proportion of accounts receivables with errors in one division (Division 1)exceeds that of the second division (Division 2).The managers believe that such a difference may exist because of the lax standards employed by the first division.To conduct the test,the accounting firm has selected random samples of accounts from each division with the following results. Based on this information and using a significance level equal to 0.05,the test statistic for the hypothesis test is approximately 1.153 and,therefore,the null hypothesis is not rejected.

The t-test for the mean difference between 2 related populations assumes that the respective:

There are a number of highly touted search engines for finding things of interest on the Internet.Recently,a consumer rating system ranked two search engines ahead of the others.Now,a computer user's magazine wishes to make the final determination regarding which one is actually better at finding particular information.To do this,each search engine was used in an attempt to locate specific information using specified keywords.Both search engines were subjected to 100 queries.Search engine 1 successfully located the information 88 times and search engine 2 located the information 80 times.Using a significance level equal to 0.05,what is the critical value for the hypothesis test?

An accounting firm has been hired by a large computer company to determine whether the proportion of accounts receivables with errors in one division (Division 1)exceeds that of the second division (Division 2).The managers believe that such a difference may exist because of the lax standards employed by the first division.To conduct the test,the accounting firm has selected random samples of accounts from each division with the following results. Based on this information and using a significance level equal to 0.05,the critical value from the standard normal table is z = 1.645.

A major U.S.oil company has developed two blends of gasoline.Managers are interested in determining whether a difference in mean gasoline mileage will be obtained from using the two blends.As part of their study,they have decided to run a test using the Chevrolet Impala automobile with automatic transmissions.They selected a random sample of 100 Impalas using Blend 1 and another 100 Impalas using Blend 2.Each car was first emptied of all the gasoline in its tank and then filled with the designated blend of the new gasoline.The car was then driven 200 miles on a specified route involving both city and highway roads.The cars were then filled and the actual miles per gallon were recorded.The following summary data were recorded: Based on the sample data,using a 0.05 level of significance,what conclusion should the company reach about whether the population mean mpg is the same or different for the two blends? Use the p-value approach to test the null hypothesis.

To find the pooled standard deviation involves taking a weighted average of the two sample variances,then finding its square root.

A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the store's in-house credit card versus using a Visa,Mastercard,or one of the other major credit cards.To do this,it has randomly selected a sample of customers who have made one or more purchases with each of the types of credit cards.The following represents the results of the sampling: Given this information,which of the following statements is true?

A recent study posed the question about whether Japanese managers are more motivated than American managers.A randomly selected sample of each was administered the Sarnoff Survey of Attitudes Toward Life (SSATL),which measures motivation for upward mobility.The SSATL scores are summarized below. Judging from the way the data were collected,which test would likely be most appropriate?

A company in Maryland has developed a device that can be attached to car engines,which it believes will increase the miles per gallon that cars will get.The owners are interested in estimating the difference between mean mpg for cars using the device versus those that are not using the device.The following data represent the mpg for random independent samples of cars from each population.The variances are assumed equal and the populations normally distributed. Given this data,what is the upper limit for a 95 percent confidence interval estimate for the difference in mean mpg?

There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account)versus single accounts (one member per account).To test this,a random sample of checking accounts was selected with the following results: Based upon these data,the critical value from the t-distribution for testing the difference between the two population means using a significance level of 0.05 is t = 1.6772.