Exam 13: Inference About Comparing Two Populations

The sampling distribution of the ratio of two sample variances is said to be F-distributed provided that we have two ____________________ samples drawn from their respective populations.

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. -{Clinic Waiting Time Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.

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. -{Senatorial Election Narrative} Can we infer at the 5% significance level that the proportions of male and female voters who intend to vote for the Democrat candidate differ?

The variance of is .

A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n₁p₁ $\ge$ 30 and n₂p₂ $\ge$ 30.

Clothing Expenditures A marketing consultant was in the process of studying the perceptions of married couples concerning their monthly clothing expenditures.He believed that the husband's perception would be higher than the wife's.To judge his belief, he takes a random sample of ten married couples and asks each spouse to estimate the family clothing expenditure (in dollars) during the previous month.The data are shown below. -{Clothing Expenditures Narrative} Can the consultant conclude at the 5% significance level that the husband's estimate is higher than the wife's estimate?

The pooled variance estimator is the ____________________ average of the two sample variances.

For testing the difference between two population proportions, the pooled proportion estimate should be used to compute the value of the test statistic when the:

____________________ samples are those for which the selection process for one is not related to the selection process for the other.

The pooled-variances t-test is used when the two population variances are ____________________.

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. -{Senatorial Election Narrative} Explain how to use the interval estimate to test the hypotheses.

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. -{Promotional Campaigns Narrative} Can they infer at the 5% significance level that sales increase during the campaign?

Engine Wear To compare the wearing of two types of automobile engines, 1 and 2, an experimenter chose to "pair" the measurements, comparing the wear for the two types of engines on each of 7 automobiles, as shown below. -(Engine Wear Narrative} Determine whether these data are sufficient to infer at the 10% significance level that the two types of engines wear differently.

When testing for the equality of two population variances the number in the null hypothesis is ____________________.

In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if the populations are normal with equal variances.

Profit Margin An investor is considering two types of investment.She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2.However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2.To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2.She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively. -{Profit Margin Narrative} Estimate with 95% confidence the ratio of the two population variances.

Given the information: the number of degrees of freedom that should be used in the pooled variance t-test is:

Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?

The test for the equality of two population variances assumes that each of the two populations is normally distributed.

A political analyst in Hawaii surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of: