Exam 13: Inference About Comparing Two Populations

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means $\mu _ { 1 } - \mu _ { 2 }$ . Assume the population variances are known. The sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ is:

We compare two population variances by examining their ____________________.

In comparing two population means of interval data, we must decide whether the samples are independent (in which case the parameter of interest is $\mu _ { 1 } - \mu _ { 2 }$ ) or matched pairs (in which case the parameter is $\mu$ _D) in order to select the correct test statistic.

When the necessary conditions are met, a two-tail test is being conducted at $\alpha$ = 0.05 to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1$ . The two sample variances are $s _ { 1 } ^ { 2 } = 400$ and $s _ { 2 } ^ { 2 } = 400$ , and the sample sizes are n₁ = 25 and n₂ = 25. The calculated value of the test statistic will be F = 2.

The test statistic for testing for the equality of two population variances has a(n) ____________________ distribution.

In constructing a confidence interval estimate for the difference between two population proportions, we ____________________ (always/sometimes/never) pool the population proportions.

Given the information: $s _ { 1 } ^ { 2 } = 4 , s _ { 2 } ^ { 2 } = 6 , n _ { 1 } = 15 , n _ { 2 } = 25,$ the number of degrees of freedom that should be used in the pooled variance t-test is:

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:

NARRBEGIN: Starting Salary Starting Salary In testing the hypotheses $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { 1 } : \mu _ { 1 } - \mu _ { 2 } \neq 0$ , two random samples from two populations of college of business graduates majoring in global marketing and international business produced the following statistics regarding their starting salaries (in $1000s): $n _ { 1 } = 50$ , $\bar { x } _ { 1 } = 35$ , $s _ { 1 } = 28$ , $n _ { 2 } = 50$ , $\bar { x } _ { 2 } = 30$ , and $s _ { 2 } = 10$ . (Assume the salaries have normal distributions.) NARREND -{Starting Salary Narrative} Explain how to use the 95% confidence interval to test the hypotheses at $\alpha$ = .05.

NARRBEGIN: Aptitude Test Scores Aptitude Test Scores Two random samples of 40 students were drawn independently from two populations of students. Assume their aptitude tests are normally distributed (total points = 100). The following statistics regarding their scores in an aptitude test were obtained: $\bar { x } _ { 1 } = 76 , s _ { 1 } = 8 , \bar { x } _ { 2 } = 72 , \text { and } s _ { 2 } = 6.5$ .NARREND -{Aptitude Test Scores Narrative} Test at the 5% significance level to determine whether we can infer that the two population means differ.

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:

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 10 pairs, is:

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} Briefly explain what the interval estimate tells you.

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} Can the statistician conclude at the 5% significance level that the required condition is not satisfied?

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} 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?

When comparing two population means using data that are gathered from a matched pairs experiment, the test statistic for $\mu$ _D is Student t-distributed with v = n_D - 1 degrees of freedom, provided that the differences are normally distributed.

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} State the null and alternative hypotheses to determine if the average number of hours until spoilage begins differs for the additives A and B.

The degrees of freedom for a test of the mean of the paired differences is the number of ____________________ minus ____________________.

The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by ____________________.

The F-test used for testing the difference in 2 population variances is always a one-tailed test.