Comparing Two Populations

 Practice Problems

To answer these questions, return to the data set of the good Dr. Wunderlich. We're going to further investigate the body temperature data. Load the data into Stata and answer these questions.

1) The data set records gender. We'll test whether there's a difference in mean body temperatures.

a) State the null and alternative hypotheses.

b) What are the assumptions? Are they satisfied here?

c) State the test and give the observed value of the test statistic.

d) What's the p-value?

e) State your conclusion.

2) Test whether pulse rates differ for men and women. (Note: although the problem seems to be asking for a simple "reject" or "not reject", your answer should include all of the components of a hypothesis test, clearly and fully stated, and not just a conclusion.)

3) The Pew Internet Project reports that Winter 2003 survey of 1358 internet users indicates that 14% of users report using music file downloaders. By way of contrast, they report, an earlier survey in the Spring of 2003 found 29% of users used a music file downloading program. In between the two surveys lots happened. For one, the music industry began suing people who used these programs, and for another Apple launched the iMusic store to sell electronic versions of music. (There were others, but Apple's was the most ambitious and successful.) Assume that the Spring survey involved 1300 internet users, and that both were random samples of the population of all internet users. The difference in figures could be due to chance -- the random element in a random sample -- or it could be "real".

a) Calculate an approximate 95% confidence interval for the change in the proportion of internet users using music downloading software.

b) Perform a hypothesis test to at a 5% significance level to test whether the proportion of users who use this software has declined.

Check your solutions!