Exam 13: Inference About Comparing Two Populations

All F-tests for the equality of two population variances are one-tailed tests.

The pooled-variances t-test requires that the two population variances need not be the same.

In testing for the equality of two population variances, when the populations are normally distributed, the 5% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of 0.05.

When the sample sizes are equal, the pooled variance of the two samples is the average of the two sample variances.

NARRBEGIN: Senatorial Election Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate.NARREND -{Senatorial Election Narrative} Estimate with 95% confidence the difference in the proportion of male and female voters who intend to vote for the Democrat candidate.

Two measurements from the same individuals is an example of data collected from a(n) ____________________ experiment.

NARRBEGIN: Fitness Program Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t-test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow: Sample 1 7 9 6 15 7 10 8 12 Sample 2 2 25 9 15 10 18 5 22 27 3 NARREND -{Fitness Program Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.

A Marine boot camp instructor recorded the time in which each of 15 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 15 degrees of freedom.

NARRBEGIN: Promotional Campaigns Promotional Campaigns The general manager of a chain of fast food chicken restaurants wants to determine how effective their promotional campaigns are. In these campaigns "20% off" coupons are widely distributed. These coupons are only valid for one week. To examine their effectiveness, the executive records the daily gross sales (in $1,000s) in one restaurant during the campaign and during the week after the campaign ends. The data is shown below. Day Sales During Campaign Sales After Campaign Sunday 18.1 16.6 Monday 10.0 8.8 Tuesday 9.1 8.6 Wednesday 8.4 8.3 Thursday 10.8 10.1 Friday 13.1 12.3 Saturday 20.8 18.9 NARREND -Motorcycle insurance appraisers examine motorcycles that have been involved in accidental collisions to assess the cost of repairs. An insurance executive is concerned that different appraisers produce significantly different assessments. In an experiment 10 motorcycles that have recently been involved in accidents were shown to two appraisers. Each assessed the estimated repair costs. These results are shown below. Can the executive conclude at the 5% significance level that the appraisers differ in their assessments? Motorcycle Appraiser 1 Apprai5er 2 1 1650 1400 2 360 380 3 640 600 4 1010 920 5 890 930 6 750 650 7 440 410 8 1210 1080 9 520 480 10 690 70

NARRBEGIN: Clinic Waiting Time Clinic Waiting Time In a random sample of 20 patients who visited a clinic at Medical Center 1, a researcher found that the variance of the waiting time (in minutes) was 128.0. In a random sample of 15 patients in the clinic of Medical Center 2, the researcher found the variance to be 178.8.NARREND -{Clinic Waiting Time Narrative} Can we infer at the 5% level of significance that the population variances differ?

NARRBEGIN: TV Sex TV Sex A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television. In a survey of 1,500 Americans, 810 believe that there is too much television sex.NARREND -{TV Sex Narrative} Estimate with 99% confidence the difference in the proportion of Canadians and Americans who believe that there is too much sex on television.

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom is:

NARRBEGIN: Promotional Campaigns Promotional Campaigns The general manager of a chain of fast food chicken restaurants wants to determine how effective their promotional campaigns are. In these campaigns "20% off" coupons are widely distributed. These coupons are only valid for one week. To examine their effectiveness, the executive records the daily gross sales (in $1,000s) in one restaurant during the campaign and during the week after the campaign ends. The data is shown below. Day Sales During Campaign Sales After Campaign Sunday 18.1 16.6 Monday 10.0 8.8 Tuesday 9.1 8.6 Wednesday 8.4 8.3 Thursday 10.8 10.1 Friday 13.1 12.3 Saturday 20.8 18.9 NARREND -{Promotional Campaigns Narrative} Estimate with 95% confidence the mean difference and interpret.

Which of the following statements is false for an F-distribution?

In constructing a confidence interval estimate for the difference between the means of two independent normally distributed populations, we:

If the F-test statistic is large, that means the variance of Population 1 is ____________________ than/to the variance of Population 2.

The t-test for the difference between the means of two independent populations assumes that the respective:

NARRBEGIN: Additives Additives A food processor wants to compare two additives for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with additive A and 16 are treated with additive B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat. The results are summarized in the table below Additive A Additive B Sample Mean 108.7 hours 98.7 hours Sample Standard Deviation 10.5 hours 13.6 hours NARREND -{Additives Narrative} Determine the rejection region at $\alpha$ = .05 and write the proper conclusion.

The sampling distribution of the ratio of two (independent) sample variances is said to be ____________________ distributed.

If you are testing to see if a weight loss program is working, and you subtract the weights before - after for a group of 10 people, the alternative hypothesis is that the mean difference is ____________________ 0.