Exam 10: Estimation and Hypothesis Testing for Two Population Parameters

There have been complaints recently from homeowners in the north end claiming that their homes have been assessed at values that are too high compared 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.Based on the information provided,the research (or alternate)hypothesis is:

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 test statistic approach to test the null hypothesis.

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 test statistic is approximately -4.22 and thus the null hypothesis should be rejected.

The t-distribution is still applicable even when there are small violations of the assumptions for the case when the variances for two populations are unknown.This is particularly true when the sample sizes are approximately equal.

Given the following information,calculate the degrees of freedom that should be used in the pooled-standard deviation t-test.

Assume that 10 people join a weight loss program for 3 months.Each person's weight both before and after the program is recorded and the number of pounds each person lost is found.The following summarizes the results for the 10 people: Mean weight lost = 9 pounds Sample standard deviation of weight lost = 4.6 pounds Assume that the hypothesis test will be conducted to determine whether or not the weight loss program is effective using a 0.05 level of significance.What is the value of the test statistic?

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 following data were reported recently where the values represent the percent moisture in the wood: Based on these data,the critical t value from the t-distribution will be 1.7459 if the significance level is set at 0.05.

A PC company uses two suppliers for rechargeable batteries for its notebook computers.Two factors are important quality features of the batteries: mean use time and variation.It is desirable that the mean use time be high and the variability be low.Recently,the PC maker conducted a test on batteries from the two suppliers.In the test,9 randomly selected batteries from Supplier 1 were tested and 12 randomly selected batteries from Supplier 2 were tested.The following results were observed: Supplier 1 Supplier 2 = 9 = 12 = 6.75 min. = 72.4 min. = 11.2 min = 9.9 min. Based on these sample results,can the PC maker conclude that a difference exists between the two batteries with respect to the population mean use time? Test using a 0.10 level of significance.

Assume that you are testing the difference in the means of two independent populations at the 0.05 level of significance.The null hypothesis is: : - ≥ 0 and you have found the test statistic is z = -1.92.What should you conclude?

A recent study posed the question about whether Japanese are managers 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. Which of the following is the correct the null and alternative hypotheses to determine if the average SSATL score of Japanese managers differs from the average SSATL score of American managers?

In estimating a confidence interval for the difference in two means,when the samples are independent and the standard deviations are unknown,it can be acceptable for there to be small violations of the assumptions of normality and equal variances,especially when the sample sizes are equal.

In estimating the difference between two population means based on small,independent samples from the two populations,two important assumptions are that the populations each be normally distributed and the populations have equal variances.

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 critical value?

A direct retailer that sells clothing on the Internet has two distribution centers and wants to determine if there is a difference between the proportion of customer order shipments that contain errors (wrong color,wrong size,etc.).It calculates a 95 percent confidence interval on the difference in the sample proportions to be -0.012 to 0.037.Based on this,it can conclude that the distribution centers differ significantly for the proportion of orders with errors.

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 responses 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.Given this,what is the appropriate null hypothesis?

Two samples are said to be independent if they are collected at different points in time.

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 pooled estimator for the overall proportion is ρ = .1050.

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,assuming that the populations are normally distributed with equal variances,the test statistic for testing whether the two populations have equal means is approximately -1.49.

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 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 is: Based on these sample data,what is the point estimate for the difference between the mean distance for the new driver versus the leading driver?

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.The sample results are: Based on these data,the point estimate is .30 hours.