Exam 11: Hypothesis Testing With Means and Proportions: The Two-Sample Case

A random sample of Toronto car commuters is compared to a random sample of Toronto bike commuters. After analyzing post-commute stress levels, researchers fail to reject the null hypothesis. Which of the following could they conclude?

How would a researcher estimate the value of the population proportion for tests of significance involving two sample proportions?

Describe two ways that researchers can meet the requirement of "independent random sampling."

When testing for the significance of the difference between two samples, what is the proper assumption for step 1?

When testing for the significance of the difference between two sample means, which of the following must be estimated before computing the test statistic?

The mean of group 1 (n = 50) is 100, and the mean of group 2 (n = 60) is 90. Both samples have a standard deviation of 20. What is the appropriate value for the test statistic?

From the population of a university, random samples of 45 graduate students and 37 undergraduate students were given a scale that measures sexual experiences. The undergraduate students report an average of 1.6 sexual partners over their lifetimes, while the graduate students report an average of 2.5 partners. The t (obtained) for this difference was -3.56, and the t (critical) was ±2.34. Which of the following can be concluded from these observations?

Which of these examples of the two-sample hypothesis test will have the greatest degrees of freedom?

Under which of these circumstances is the assumption of equal population variance safe to assume in a two-sample hypothesis test?

Researchers conduct a test of mean differences using the t distribution with sample sizes of 30 and 35. The researchers specify a two-tailed test and set alpha at 0.05. What is the degrees of freedom they need to obtain the critical value for their test?

Which of these sets of samples would qualify as meeting the assumption of sample size equality for calculating a "pooled estimate" in a two-sample hypothesis test?

Two sets of 95% confidence intervals correspond to a random sample of two groups: group A: c.i. = 6.5 ± 0.5; group B: c.i. = 7.4 ± 0.2. Which of the following could we conclude about the mean differences of the groups with these confidence intervals?

What pieces of information from two samples does the "pooled estimate" combine?

A test was conducted for the significance of the difference in average education for random samples of males and females in Canada. Males received an average of 13.67 years of schooling and females received an average of 14.05 years. The obtained Z score for this difference was -59.9. Based on these results, which of the following is a reasonable conclusion?

Explain the meaning of the "null hypothesis" for a two-sample test of means or proportions.

When testing for the significance of the difference between sample means when (sigma) is unknown, which of the following is the proper sampling distribution?

An economist wishes to compare retirement savings of public sector workers to private sector workers. What type of hypothesis test should she employ?

Random samples of 145 men and 237 women from a university were asked if they had ever cheated in one of their courses. Eight percent of the men and 6% of the women said that they had cheated. Which is the appropriate test for assessing the significance of this difference?

Two sets of 95% confidence intervals correspond to proportions calculated from a random sample of two groups: group A: c.i. = 0.64 ± 0.06; group B: c.i. = 0.61 ± 0.05. Which of the following could we conclude about the proportion differences of the groups with these confidence intervals?

Which of these variables would be appropriate for testing the difference between two sample means?