Exam 10: Estimation and Hypothesis Testing for Two Population Parameters

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: Suppose that the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards,using a significance level of .05,what is the value of the test statistic assuming the standard deviations are known?

Suppose a survey is taken of two groups of people where each person is asked a yes/no question and the proportion of people who answer yes is calculated for each group.Which of the following is true about a hypothesis test of the difference in the two proportions?

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses.They want 95 percent confidence and will select a sample of 10 men and 10 women for the study.If the NCAA assumes that the population standard deviations are known,the critical value for the confidence interval is t = 2.1009.

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 company can conclude that there is a statistical difference between men and women with regard to mean spending at the hardware store with men tending to spend more on average than women.

In order to make the test for the difference between two population means valid,the sample size in each independent sample must be the same.

Most companies that make golf balls and golf clubs use a one-armed robot named "Iron Mike" 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 the critical value for the appropriate hypothesis test if the test is conducted using a 0.05 level of significance?

When performing a hypothesis test for the difference in the means of two independent populations,where the standard deviations are known,the variances must be assumed equal.

A major U.S.oil company has developed two blends of gasoline.Managers are interested in estimating the difference in mean gasoline mileage that 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 these sample data,compute and interpret the 95 percent confidence interval estimate for the difference in mean mpg for the two blends.

The test statistic that is used when testing hypotheses about the difference between two population proportions is the t-value from the t-distribution.

A real estate agent believes that home with swimming pools take longer to sell than home without swimming pools.A random sample of each type of recently sold homes was taken where the number of days on the market is recorded.Results are: Assuming that the populations are normally distributed and the variances are equal,conduct the appropriate hypothesis test to determine if the real estate agent is correct.Use the 0.05 level of significance.

If the sample data lead us to suspect that the variances of the two populations are not equal,the t-test statistic and the degrees of freedom must be adjusted accordingly.

The t-distribution can be used to test hypotheses about the difference between two population means given the following two assumptions: - each population is normally distributed,and - the two populations have equal variances.

If you are interested in estimating the difference between the means of two samples that have been paired,the point estimate for this difference is the mean value of the paired differences.

A maker of toothpaste is interested in testing whether the proportion of adults (over age 18)who use its toothpaste and have no cavities within a six-month period is any different than the proportion of children (18 and under)who use the toothpaste and have no cavities within a six-month period.To test this,it has selected a sample of adults and a sample of children randomly from the population of those customers who use their toothpaste.The following results were observed. Adults Children Sample Size 100 200 Number with 0 cavities 83 165 Based on these sample data and using a significance level of 0.05,what conclusion should be reached? Use the p-value approach to conduct the test.

A market research firm has come up with two coupon designs that could be inserted into the envelopes that go out with the monthly statement to credit card customers.The coupons offer the customer an opportunity to become a member of a travel club.The research firm is interested in estimating the difference in proportion of customers who will join the club after receiving one or the other of the two coupons.To obtain this estimate,the research firm has sent out coupon design 1 to a random sample of 100 customers.A second random sample of 100 customers received coupon 2.For the first coupon,11 customers joined the travel club,while 15 customers who received coupon 2 joined.Based upon this sample information,develop and interpret the desired 95 percent confidence interval estimate.

To find a confidence interval on the difference between the means of independent samples,when the variances are unknown but assumed equal,the sample sizes of the two groups must be the same.

The Sergio Lumber Company manufacturers plywood.One step in the process is the one where the veneer is dried by passing through a huge dryer (similar to an oven)where much of the moisture in the veneer is extracted.At the end of this step,samples of veneer are tested for moisture content.It is believed that pine veneer will be less moist on average than will fir veneer.The hypothesis test that will be conducted using an alpha = 0.05 level will be a two-tailed test.

Increasing the size of the samples in a study to estimate the difference between two population means will increase the level of confidence that a decision maker can have regarding the interval estimate.

In conducting a hypothesis test for the difference in two population means where the standard deviations are known and the null hypothesis is: : - ≥ 0 What is the p-value assuming that the test statistic has been found to be z = 2.52?

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 independent random samples of cars from each population.The variances are assumed equal and the populations normally distributed. Given this data,what is the critical value if the owners wish to have a 90 percent confidence interval estimate?