Exam 12: Inference About Comparing Two Populations, Part 1

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: . -Estimate with 95% confidence the difference between the two population means.

Suppose we randomly selected 250 people, and on the basis of their responses to a survey we assigned them to one of two groups: high-risk group and low-risk group. We then recorded the blood pressure for the members of each group. Such data are called:

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.

The expected value of is .

Unless we can conclude that the population variances are equal, we cannot use the pooled variance estimate.

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

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

In testing the difference between the means of two normally distributed populations, the number of degrees of freedom associated with the unequal-variances t-test statistic usually results in a non-integer number. It is recommended that you:

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

A calculus professor wanted to test whether the grades on calculus test were the same for upper and lower classmen. The professor took a random sample of size 12 from each group. For this situation, the professor should use a matched pairs t-test.

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

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.

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

Undergraduates' Test Scores: 35 undergraduate students who completed two years of college were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 students who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively -Can we infer at the 10% significance level that a difference exists between the two groups?

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:

The sampling distribution of is normal if the sampled populations are normal, and approximately normal if the populations are nonnormal and the sample sizes n₁ and n₂ are large.

What conclusion can we draw at the 5% significance level?

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

When the population variances are unknown and unequal, we estimate each population variance with its ____________________ variance.

A matched pairs experiment decreases variability (compared to two independent samples).