Exam 10: Estimation and Hypothesis Testing for Two Population Parameters

When estimating a confidence interval for the difference between 2 means using the method where sample variances are pooled,which of the following assumptions is not needed?

The U.S.Golf Association provides a number of services for its members.One of these is the evaluation of golf equipment to make sure that the equipment satisfies the rules of golf.For example,they regularly test the golf balls made by the various companies that sell balls in the United States.Recently they undertook a study of two brands of golf balls with the objective to see whether there is a difference in the mean distance that the two golf ball brands will fly off the tee.To conduct the test,the U.S.G.A.uses a robot named "Iron Byron," which swings the club at the same speed and with the same swing pattern each time it is used.The following data reflect sample data for a random sample of balls of each brand. Given this information,what is the test statistic for testing whether the two population means are equal?

Most companies that make golf balls and golf clubs use a one-armed robot named "Iron Byron" to test their balls for length and accuracy,but because of swing variations by real golfers,these test robots don't always indicate how the clubs will perform in actual use.One company in the golfing industry is interested in testing its new driver to see how it compares with the best-selling driver.To do this,it has selected a group of golfers of differing abilities and ages.Its plan is to have each player use each of the two clubs and hit five balls.It will record the average length of the drives with each club for each player.Given this description of the planned test,which of the following statements is true?

Under what conditions can the t-distribution be correctly employed to test the difference between two population means?

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.Assume that the variances are equal and the populations normally distributed.The following data represent independent samples from each population: Based on these data,the upper limit of the interval estimate is approximately $13.82.

In comparing two populations using paired differences,after the difference is found for each pair,the method for testing whether the mean difference is equal to 0 becomes the same as was used for a one-group hypothesis test with unknown standard deviation.

Two placement exams are available that students can take to determine which math class they should begin with in their freshman year.It is believed that there is no difference in the mean scores that would be received for the two tests.To test this using a 0.05 level of significance,a randomly selected group of students took both tests and had their scores recorded.The following data were obtained: Based on these data,the test statistic is approximately t = -1.892.

The management of a department store is interested to estimate the difference in the amount of money spent by female and male shoppers.You are given the following information. A 95 percent confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses.It wants 95 percent confidence and will select a sample of 10 men and 10 women for the study.The variances are assumed equal and the populations normally distributed.The sample results are: Based on these sample data,the estimate for the standard deviation of the sampling distribution is found by taking the square root of the sum of the two sample variances.

A hypothesis test for the difference between two means is considered a two-tailed test when:

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: Based on these sample data,what is the lower limit for the 95 percent confidence interval estimate for the difference between population means?

A commuter has two different routes available to drive to work.She wants to test whether route A is faster than route B.The best hypotheses are:

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 null hypothesis to be tested?

Most companies that make golf balls and golf clubs use a one-armed robot named "Iron Byron" to test their balls for length and accuracy,but because of swing variations by real golfers,these test robots don't always indicate how the clubs will perform in actual use.One company in the golfing industry is interested in testing its new driver to see if it has greater length off the tee than the best-selling driver.To do this,it has selected a group of golfers of differing abilities and ages.Its plan is to have each player use each of the two clubs and hit five balls.It will record the average length of the drives with each club for each player.The resulting data for a sample of 10 players are: What is an appropriate null hypothesis to be tested?

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses.It wants 95 percent confidence and will select a sample of 10 men and 10 women for the study.The variances are assumed equal and the populations normally distributed.The sample results are: Based on these sample data,the critical value for developing the confidence interval is z = 1.96.

If the population variances are assumed to be known in an application where a manager wishes to estimate the difference between two population means,the 95 percent confidence interval estimate can be developed using which of the following critical values:

If we are testing for the difference between the means of two paired populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to:

A study was recently conducted at a major university to determine whether there is a 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 these sample data,and testing at the 0.10 level of significance,what is the value of the test statistic?

If the point estimate in a paired difference estimation example does not fall in the resulting confidence interval,the decision maker can conclude that the two populations likely have different means.

A major manufacturer of home electronics is interested in determining whether customers have a preference between two new speaker designs for their home entertainment centers.To test this,the design department manager has selected a random sample of customers and shown them the first design.A second sample of customers is shown design 2.The manager then asks each customer whether they prefer the new design they were shown over the one they currently own.The following results were observed: Based on these data and a significance level equal to 0.05,the appropriate null and alternative hypotheses are: