STAT 301 - Business Statistics
Lecture Review #24 - Independent Proportions

Review questions:

1) What distinguishes independent samples from paired data?

2) What is the basic concept underlying the analysis of data from two independent samples?

Computational exercises:

1) The "gender gap" in American politics is the phenomenon that women tend to be more likely to support Democrat candidates, while men are more likely to support Republicans. A recent survey of adults nationwide was conducted to investigate people's opinions on a variety of political and social issues. One question on the survey was: Do you tend to associate yourself more with the philosophies and policies of the Democrat or the Republican party? Of 800 women responding to the question, 440 indicated greater agreement with the Democrat party, while 380 of the 800 men did. Find a 95% confidence interval for the size of the "gender gap," as measured by the survey question.

2) Clyde Arthur Fazenbaker, as a research project for his statistics class, wonders whether sleeping with a statistics book under the pillow will help one absorb the material by osmosis. He recruits fifty of his friends to assist him in his study. Half of them (chosen at random) sleep the night before the "big quiz" with the statistics book under their pillow. The other half serve as a control group. They sleep with a placebo book under the pillow. Of the 25 with the statistics book, 20 got good grades (C or higher) on the "big quiz." Fifteen of the 25 in the control group got grades of C or higher. Find a 95% confidence interval for the difference between the two population proportions. Interpret this result. Can we say (with 95% confidence), based upon this experiment, that sleeping with the book under your pillow is a good strategy? Why?

SOLUTIONS:
1) 0.075 + 0.049
2) z = 1.543