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Review Material

Problem 1 (20pt.): An insurance company gives a table of insurance payments for 20 clients over the period of one year (the payments are ordered from the smallest to the largest, and measured in dollars):

(a) (4) Determine the median insurance payment.

(b) (4) Without doing any calculations, how do you expect the mean insurance payment to compare to the median insurance payment? Explain.

(c) (4) Use technology to compute the mean of insurance payments.

(d) (4) Did your calculation confirm your prediction from the part (b)? Are the mean and median close to each other? Explain why this makes sense.

(e) (4) If the managers of the insurance company want to advertise either the mean or median insurance payment in order to give the impression that the company pays huge amounts of money to the hospitals for its clients, which (mean or median) should they advertise? Explain.

Problem 2 (20pt.): Let the random variable X be the number of reported fires in a small town over the span of one week. The discrete probability distribution of X is shown in a table below.

(a) (5) Verify the two main requirements that make this a legitimate discrete probability distribution.

(b) (5) Explain in words what the probability means. What is the probability ?

(c) (5) Compute the expected value of the random variable .

(d) (5) Compute the standard deviation of the random variable .

New Material

Problem 3 (20pt.): A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for the second time. They show the movie to a test audience of 200 people, and after the movie they asked them if they would see the movie in theaters again. Of the test audience, 68 people said that they would see the movie again.

(a) (5) Describe the population of interest ( 2 points ) and calculate the numerical value of the statistic  that that we will use to estimate the proportion of viewers who will return to see the movie ( 3 points ).

(b) (5) Construct a 95% confidence interval for the proportion of viewers who will return to see the movie.

(c) (5) Construct a 99% confidence interval for the proportion of viewers who will return to see the movie.

(d) (5) Describe the relationship between the level of confidence and the size of the confidence interval .

Problem 4 (20pt.): A farmer is concerned that a change in fertilizer to an organic variant might reduce the crop yield. He subdivides 6 lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half. The following table shows the results.

(a) (4) Which two-sample test should you use for this situation?

(b) (16) Is there enough evidence to conclude that the new fertilizer reduced the yield? Use the level of significance . You must state the hypotheses (4 points), determine the test statistic (4 points), and either the P-value(s) or critical value(s) (4 points). Finally, you must clearly state your conclusion (4 points) . Round all computations and answers to four decimal places.

Problem 5 (20pt.): Some researchers believe that boys are more likely than girls to grow out of childhood asthma when they hit their teenage years. Scientists followed 400 boys and 600 girls between the ages 5 and 12, all of whom had mild to moderate asthma in the beginning. By the age of 18, 85 girls and 118 boys seemed to have grown out of asthma.

(a) (4) Which two-sample test should you use for this situation?

(b)