1. Yankelovich partners, Inc., conducted a survey in May 1995 for Time/CNN to examine opinions of American adults on reducing the federal budget deficit (Time, May 22, 1995). Twenty percent of the adults polled were in favor of eliminating the U.S. Department of Education. Assume this result is true for the current population of all American adults.

a. Find the mean and standard deviation of the number of adults who would be in favor of eliminating the U.S. Department of Education in a sample of 12 adults.

b. Find the probability that in a random sample of 12 American adults the number who would favor eliminating the Department of Education is at least 6.

c. Find the mean and standard deviation of the proportion in a random sample of 200 American adults who would favor eliminating the Department of Education.

d. Used the Normal approximation to find the probability that the proportion of American adults who would favor eliminating the Department of Education in a random sample of 200 will be between 0.17 and 0.23.

2. According to a Priority management survey, adults spend an average of 10 hours a day at work and commuting. Let the daily work and commute times for all adults have a normal distribution with a mean of 10 hours and a standard deviation of 1.8 hours.

a. What is the probability that the daily work and commute time for a randomly selected adult will be more than 13 hours?

b. Find the probability that the mean of the daily work and commute times for a random sample of 80 adults will be between 9.75 and 10.50 hours.

3. A study is to be conducted on the mean salary of mayors of cities with populations of fewer than 100,000. The margin of error in estimating the mean is to be less than $100, and a confidence level of 99% is desired. Suppose the standard deviation of the population is $1000. What is the required sample size?

4. A test was constructed to measure the degree of people’s alienation. the mean score was 78 and the standard deviation of scores in the population was 16. The test was administered to a sample of 37 Gulf War veterans. Their mean score was 84.

a. At the 0.05 significance level, can we conclude that Gulf War veterans are more alienated than the general population?

(In answering this question:

State the null and alternative hypothesis

Find the P-Value and report your conclusions.)

b. Set up a 95% confidence interval for the mean alienation score of the Gulf War veterans.

5. A study dealing with divorced couples gathered data on the length of time from marriage to separation. A random sample of 30 divorced couples had an average length of marriage of 5.9 years, with a sample standard deviation of 2.0 years.

a. Construct a 99% confidence interval for the mean length of time from marriage to separation for the population of divorced couples.