1. Comparing Proportions (15 points)

Supposethat you areinterested in determining whetherthe advicegiven bya physicianduring aroutine physicalexamination is effectivein encouraging patients to stopsmoking. In astudy ofcurrentsmokers, one groupof patients wasgiven abrief talkabout the hazards ofsmoking and was encouragedto quit. A second groupreceived noadvicepertaining to smoking. All patients weregiven afollow-upexam.Inthe sampleof114 patients who had received the advice, 11 reported that they had quit smoking; inthesampleof 96 patients who had not, 7 had quit smoking.

1. Writethe null and alternativehypothesis fortesting the differencebetweenthesetwo proportions. (2 pts)
2. What arethe critical values and rejection region for this test if your alpha is 0.05?(2 pts)
3. Calculate thetest statistic forthe differencebetween the proportions. (4 pts)
4. UseSAS to get thep-valueforthis test and reportthe number here. (1 pt)
5. Do you reject thenull hypothesis or not? Why? (2pts)
6. Writeameaningful conclusionforyour decision about thenull hypothesis.(1 pt)
7. Construct a 95%confidence intervalforthe difference between thesetwoproportions. (3 pts)

2. Comparing Means (13 points)

Nowsuppose that you are interested in determining whethertheadvicegiven byaphysician during a routine physicalexamination iseffective in encouragingobesepatients to lose weight. In thesample of 36patients who received the advice, the averagedecrease in BMIwas 5 points with a standard deviation of 1.25 points. You wantto knowif this changeis significantlydifferent than theexpected decrease of 3points.

1. Writethe null and alternativehypothesis fortesting the differencebetweenthismean and the null hypothesis mean of 3points. (2pts)
2. Calculate thetest statisticforthe t-test of onemean. (4pts)
3. UseSAS to get thep-valueforthis test and reportthe number here. (1 pt)
4. Do you reject thenull hypothesis or not? Why? (2pts)
5. Writeameaningful conclusion foryour decision about thenull hypothesis.(1 pt)
6. Construct a 95%confidence intervalforthe mean. (3 pts)