1.

Rap music is more popular among young blacks than among young whites. A sample survey compared 604 randomly chosen blacks aged 15 to 25 with 578 randomly selected whites in the same age group. It found that 345 of the blacks and 121 of the whites listened to rap music every day. Give a 99.5% large-sample confidence interval for the difference between the proportions of black and white young people who listen to rap every day.

Interval:( )to( )

2.In 2002 the Supreme Court ruled that schools could require random drug tests of students participating in competitive after-school activities such as athletics. Does drug testing reduce use of illegal drugs? A study compared two similar high schools in Oregon. Wahtonka High School tested athletes at random and Warrenton High School did not. In a confidential survey, 6 of 100 athletes at Wahtonka and 24 of 132 athletes at Warrenton said they were using drugs. Regard these athletes as SRSs from the populations of athletes at similar schools with and without drug testing.

(b) The plus four method adds two observations, a success and a failure, to each sample. What are the sample sizes and the numbers of drug users after you do this?

Wahtonka sample size:( ) Wahtonka drug users:( ) Warrenton sample size:( ) Warrenton drug users:( )

(c) Give the plus four 96% confidence interval for the difference between the proportion of athletes using drugs at schools with and without testing. Interval:( )to( )

3.

Independent random samples, each containing 50 observations, were selected from two populations. The samples from populations 1 and 2 produced 24 and 19 successes, respectively.

TestH0:(p1p2)=0 againstHa:(p1p2)0. Use=0.04.

(a) The test statistic is( )

(b) The P-value is( )

4.

In a study of red/green color blindness, 750 men and 2700 women are randomly selected and tested. Among the men, 66 have red/green color blindness. Among the women, 8 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.

(Note: Typep_mfor the symbolpm, for examplep_mnot=p_wfor the proportions are not equal,p_m>p_wfor the proportion of men with color blindness is larger,p_m

(a) State the null hypothesis:( )

(b) State the alternative hypothesis:( )

(c) The test statistic is( )

(e) Construct the90% confidence interval for the difference between the color blindness rates of men and women.

( )<(pmpw)<( )

5.

Suppose a group of 800 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 305 patients who received the antidepressant drug, 75 were not smoking one year later. Of the 495 patients who received the placebo, 39 were not smoking one year later. Given the null hypothesisH0:(pdrugpplacebo)=0and the alternative hypothesisHa:(pdrugpplacebo)0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use=0.03,

(a) The test statistic is( )

(b) The P-value is( )

6.

(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume the "worst case" scenario for the value of both sample proportions. We want a98% confidence level and for the error to be smaller than0.01.

Answer:

(b) Again find the sample size required, as in part (a), but with the knowledge that a similar student last year found that the proportion of boys afraid of spiders is 0.62 and the proportion of girls afraid of spiders was 0.64.

Answer:

7.

Never forget that even small effects can be statistically significant if the samples are large. To illustrate this fact, consider a sample of 130 small businesses. During a three-year period, 14 of the 101 headed by men and 5 of the 29 headed by women failed.

(a) Find the proportions of failures for businesses headed by women and businesses headed by men. These sample proportions are quite close to each other. Give the P-value for the test of the hypothesis that the same proportion of women's and men's businesses fail. (Use the two-sided alternative). What can we conclude (Use=0.05)? The P-value was( )

(b) Now suppose that the same sample proportion came from a sample 30 times as large. That is, 150 out of 870 businesses headed by women and 420 out of 3030 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in part (a). Repeat the test for the new data. What can we conclude? The P-value was( )

(c) It is wise to use a confidence interval to estimate the size of an effect rather than just giving a P-value. Give 95% confidence intervals for the difference between proportions of men's and women's businesses (men minus women) that fail for the settings of both (a) and (b). (Be sure to check that the conditions are met. If the conditions aren't met for one of the intervals, use the same type of interval for both) Interval for smaller samples:( )to( ) Interval for larger samples:( )to( )