Exam 13: Inference About Comparing Two Populations

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: . ​ ​ -{Aptitude Test Scores Narrative} Explain how to use the 95% confidence interval to test the hypotheses at α = .05.

In comparing the difference in means with a matched pairs experiment,the variable under consideration is ,where the subscript D refers to the difference.

In testing the difference between two population means using two independent samples,the sampling distribution of the sample mean difference is normal if the sample sizes are both greater than 30.

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

If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2,the second observation of sample 1 with the second observation of sample 2,and so on,the samples are referred to as:

The test for the mean difference in a matched pairs design requires the differences to have a(n)____________________ distribution.

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

The F-distribution is the sampling distribution of the ratio of:

In comparing two population means the statistic under consideration is .

The variance of the difference between two sample proportions equals the ____________________ of their population proportion variances.

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

The test statistic employed to test is F-distributed with v₁ = n₁ − 1 and v₂ = n₂ − 1 degrees of freedom if the two populations are F-distributed.

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:

In testing the hypothesis ,two random samples from two normal populations produced the following statistics: .What conclusion can we draw at the 1% significance level?

The expected value of the difference between two sample proportions is the difference between their corresponding population proportions.

A political analyst in Iowa 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 ____________________ samples.

Worker Safety An OSHA agent wanted to determine if efforts to promote safety have been successful.By checking the records of 250 workers,he found that 30 of them suffered either minor or major injuries that year.A random sample of 400 workers last year revealed that 80 suffered some form of injury. ​ ​ -{Worker Safety Narrative} Can the statistician infer at the 5% significance level that efforts to promote safety have been successful?

In a matched pairs experiment the parameter of interest is the ____________________ of the population of ____________________.

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. ​ ​ -{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.

The ratio of two independent chi-squared variables divided by their degrees of freedom is: