1.[12 points] Assume that ages of moviegoers are normally distributed with a mean of 35 years and a standard deviation of 20 years.

a.What is the percentage of moviegoers who are younger than 30 years of age.

b.Find ,which is the 25^th percentiles.

c.Find the probability that a simple random sample of 25 moviegoers has a mean age that is less than 30 years.

d.Find the probability that the simple random sample of 25 moviegoers, each of the moviegoers is younger than 30 years of age. For a particular movie and showtime, why might it not be unusual to have 25 moviegoers all under the age of 30.

2.[ 12 points] In a survey sponsored by Lindt chocolate company,1708 women were surveyed and 85% of them said that chocolate made them happier.

a.Is there anything potentially wrong with this survey? Explain.

b.Construct a 99% confidence interval estimate the percentage of women who say that chocolate makes them happier. write a brief statement interpreting the results.

In the process of constructing the confidence interval identify the best point estimate and calculate the margin of error using the formula from section 7.2

c.Test the claim that when asked more than 80% of women say that chocolate makes them happier. Use a 0.01 significance level.

Hint: Refer to Chapter 8-9 outline, follow the instructions to test using the

critical value method.

3.[8 points] You plan to conduct a survey to estimate the percentage of adults who have had chickenpox. Find the number of people who must be surveyed if you want to be 90% confident that the sample percentage within two percentage points of the true percentage for the population of all the adults.

a. Assume that nothing is known about the prevalence of chickenpox.

b. Assume that about 95% of adults have had chickenpox.

4.[8 points ] A number of fetal stem cells may cross the placenta from the fetus to the mother during pregnancy and remain in the mother's tissue for decades. A recent study shows that the presence of fetal cells in the mother may offer some protection against onset of breast cancer. Of the 54 women in a study with breast cancer, 14 had fetal cells. Of the 45 women without breast cancer 25 had fetal cells. Test the claim whether there is a difference in the population proportions of women who had fetal cells, using level of significance , Use the criticalmethod.

a.Hypotheses:H_o:H₁:

b.Test statistic: (from your calculator)

c.Critical value:

d.Decision: Reject or fail to reject? Why?

e.Write your decision in a sentence in the context of the problem?

5.[ 8 points] The ACT is a college entrance exam; the ACT has determined that a score of 22 on mathematics portion of the ACT suggested that a student is ready for college level mathematics. To achieve this goal, ACT recommends that students take a core curriculum of math courses. Suppose a sample of 200 students who completed this core set of courses results in a mean ACT math score of 22.6 with standard deviation 3.9. Do these results suggest that students who complete the core curriculum are ready for college-level math? That is, are they scoring above 22 on math portion of the ACT?

a.State the appropriate null and alternative hypothesis?

b.Use the P value method to test the hypothesis in part a.

c.Write a conclusion based on your results.