Exam 11: Hypothesis Tests Involving Two Sample Means

Price earnings A comparison of the price-earnings (P/E)ratio for the top and bottom 100 companies in valuation is being prepared.A financial advisor randomly sampled each group to determine whether there is any difference in P/E ratios of the two groups of companies.Let 1 = a top 100 company and 2 = a bottom 100 company.Assume equal population variances and that the populations are normally distributed.The advisor is to use a 0.01 significance level.The data were randomly selected and are summarized below: Top 100 company Bottom 100 company =6 =6 =18.83 =10.67 =128.17 =8.67 -State the null and alternative hypotheses. H₀: ____________________ H₁: ____________________

Traffic Coordinator A traffic coordinator for a community wishes to determine whether or not there is any difference in the average age of female and male drivers involved in rear-end accidents.The hypothesis test is: H₀: $\mu _ { 1 } = \mu _ { 2 }$ (no difference in mean age) H₁: $\mu _ { 1 } \neq \mu _ { 2 }$ (mean age is different)A random sample of males and females involved in rear-end accidents results in the following Minitab summary: N MEAN MEDIAN TRMEAN STDEV SEMEAN FEMALES 33 23.91 20.00 23.38 9.77 1.70 MALES 38 28.87 28.50 28.44 9.67 1.57 What is the standard error of the difference between the two means?

Textbook A large textbook publisher is concerned about the sale of complimentary desk copies of textbooks to wholesale book buyers.The publisher randomly samples the faculty from two universities,A and B.Information provided by salespeople suggests that the faculty at University A had copies of the publisher's books that had been shipped,whereas the faculty at University B seldomly had them.Let $\pi _ { 1 }$ be the proportion of faculty at University A who sell this publisher's books and $\pi _ { 2 }$ be the proportion of faculty at University B who sell this publisher's books.The samples provide these data: At the 0.05 significance level,is this publisher reasonably justified in saying there is a higher proportion of faculty at University B who sell this publisher's complimentary books than at University A? -State the decision rule.

Production Line A quality control inspector keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines.The completed sheet is shown below. Products Production line Acceptable Unacceptable 1 152 48 2 136 54 -Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2? Hypotheses: ___________________________________ Test statistic = ________ Conclusion: ________________ Interpretation: __________________________________________________

Realtor A new realtor in a large community is attempting to determine differences in the selling prices of houses in two sections of the community.Population 1 is the Northeast and Population 2 is the Southwest.The realtor is going to perform the hypothesis test: H₀: $\mu _ { 1 } = \mu _ { 2 }$ H₁: $\mu _ { 1 } \neq \mu _ { 2 }$ A random sample of 35 sale homes is taken from the Northeast and 41 from those in the Southwest using the multiple listing services.A Minitab summary of the results of the two samples expressed in thousands follows: N MEAN MEDIAN TRMEAN STDEV SE MEAN NORTHEAST 35 86.789 84.800 88.313 60.067 10.153 SOUTHWEST 41 60.490 62.200 61.857 14.740 2.302 -What is the conclusion?

Chrysler corp Chrysler Corp.is responding to an advertisement by Toyota,which claims that its compact version gets much better gasoline mileage for in-city driving than any U.S.made car.Below are the results of surveys conducted to test the claim.Perform the appropriate test at the 0.01 significance level. Toyota Clurysler =30 =30 =24 =22.9 =91.28 =169.3 What is the p-value?

Chrysler corp Chrysler Corp.is responding to an advertisement by Toyota,which claims that its compact version gets much better gasoline mileage for in-city driving than any U.S.made car.Below are the results of surveys conducted to test the claim.Perform the appropriate test at the 0.01 significance level. Toyota Clurysler =30 =30 =24 =22.9 =91.28 =169.3 -What is the test statistic? Appropriate test: ____________________ Test statistic = ____________________

Women drivers In the past,young women drivers have maintained a better driving record than young men drivers.An insurance company is concerned with the driving record of its insured customers.Specifically,it conducts a test for the number of speeding tickets received during the past year by drivers between the ages of 18 and 25. Men Women =120 =85 =1.2 =0.4 =24.8 =10.6 A test for the equality of average number of tickets per driver for the two groups is desired.Use $\alpha$ = 0.01.Calculate the p-value for this test.

Shooting club A trap and skeet shooting club purchases clay pigeons.These are quite fragile and often break in the box during shipment without any outward sign of breakage.Even as the pigeons are loaded into the throwing machine,broken or cracked pigeons may not be noticed.Each pigeon broken is a net loss to the club so the club is anxious to purchase from suppliers who have a record of little or no breakage in shipping and handling.Two suppliers of clay pigeons are contacted and asked for price quotes.Supplier 1 quotes a higher price than Supplier 2 but says that the higher price is the result of better packaging and thus more usable pigeons per case.The shooting club manager decides to purchase 10 cases from both suppliers.Each case has 250 pigeons.Careful records are maintained on each case as to the number of good pigeons.The records after the cases were used are as follows: Number of good pigeons Supplier 1 Supplier 2 234 222 237 225 240 219 241 221 234 218 235 226 241 230 246 219 240 208 243 213 -Use Excel or Minitab to conduct a two-sample t-test Test the hypotheses: H₀: $\mu$ ₁ $\le$ $\mu$ ₂ H₁: $\mu$ ₁ > $\mu$ ₂ at the 5% significance level.What is your conclusion?