1.

2.5758

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 99% confidence interval for the proportion who are not satisfied.

(a) Past studies suggest that this proportion will be about 0.29. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.025.

(You will need a critical value accurate to at least 4 decimal places.)

Sample size:

(b) Using the sample size above, when the sample is actually contacted, 22% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

MoE:

2.

Two random samples are taken, one from among first-year UVA students and the other from among fourth-year UVA students. Both samples are asked if they favor modifying the Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below:

First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=94,n2=83,x1=56x2=50

First-Years (Pop. 1):n1=94,x1=56Fourth-Years (Pop. 2):n2=83,x2=50

Is there evidence, at an =0.08=0.08 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

B. The p-value is

3.

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 103 athletes at Wahtonka and 23 of 102 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.

(a) 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:

(b) Give the plus four 99.8% confidence interval for the difference between the proportion of athletes using drugs at schools with and without testing.

Interval:

4.

Two random samples are taken, with each group asked if they support a particular candidate. A summary of the sample sizes and proportions of each group answering yes'' are given below:

Pop. 1:Pop. 2:n1=89,n2=95,p^1=0.813p^2=0.582

Pop. 1:n1=89,p^1=0.813Pop. 2:n2=95,p^2=0.582

Suppose that the data yields (0.0865, 0.3755) for a confidence interval for the difference p1p2p1p2 of the population proportions. What is the confidence level? (Give your answer in terms of percentages.)

Confidence Level =