1. Recall the survey you took during the first week of class. One of the questions was "do you agree that it is inappropriate to speak on a cellphone while at a restaurant?" Of the 1913 females that responded to the survey, 1729 agreed with this statement. Of the 1276 males that responded to this survey, 1111 agreed with this statement. Test to see if there is any difference between males and females with respect to how they feel about this issue. Use a significance level of .05.

1. (a)State the appropriate null and alternative hypotheses.
2. (b)Calculate the test statistic and report the p-value.
3. (c)State your conclusion in context of the problem.
4. (d)Based only on the results of the hypothesis test, would you expect a 95% confidence interval to include 0? Explain.
5. (e)Calculate and interpret a 95% confidence interval for the difference between males and females.

2. In a recent baseball World Series, the Houston Astros were ordered to keep the roof of their stadium open. The Houston team claimed that this would make them lose a home-field advantage, because the noise from fans would be less effective. During the regular season, Houston won 36 of 53 games played with the roof closed, and they won 15 of 26 games played with the roof open. Treat these results as a simple random sample of games. Use a significance level of 0.05 to test the claim that the proportion of wins at home is higher with a closed roof than with an open roof. Does the closed roof appear to be an advantage?

1. (a)State the null and alternative hypotheses to determine whether the closed roof is an advantage.
2. (b)The test statistic for the above test was z = 0.89 which gives us a p-value of 0.1858. State a conclusion in context of the problem.
3. (c)Based on the results of the hypothesis test, would you expect a confidence interval to include 0. Why or why not?

3. In a study of the effects of marijuana use during pregnancy, measurements on babies of mothers who used marijuana during pregnancy were compared to measurements on babies of mothers who did not. A 95% confidence interval for the difference in mean head circumference 1 2 (1 is mean for mothers who don't use marijuana and 2 is the mean for mothers who use marijuana) was 0.61 to 1.19 cm.

1. (a)Interpret this confidence interval in context of the problem.
2. (b)Based on the confidence interval, what can we say about the p-value of the following hypothesis test: H0 : 1 = 2 versus H1 : 1 > 2 at the 0.05 significance level? State your conclusion for the test.