STAT

STAT 350 (Spring 2017) Homework 7 (20 points) 1

Practice Problems: 8.1 (p.338), 8.3 (p.338), 8.5 (p.338) (1 pt.) 1. The graph below shows the probability density functions for three different statistics

that could be used to estimate a population parameter θ. Which statistic would you use and why?

Practice Problems: 8.19 (p.349), 8.21 (p.349), 8.23 (p.349) (6 pts.) 2. The owner of a small tailoring shop keeps careful records of all alterations. A

common alteration to men’s clothing is lengthening the inseam on pants A random sample of 33 pants was obtained, and the amount lengthened on the inseam was recorded. The measured mean was 0.74 inches. Assume σ = 0.22 inches..

(1 pt.) a) What assumptions are required so that you can construct a confidence interval for the mean alteration of the inseam?

(1 pt.) b) Find a 99% confidence interval for the mean alternation of the inseams on men's pants.

(1 pt.) c) Interpret your answer in part b). (2 pts.) d) There is a maximum amount that any pair of pants can be lengthened. Therefore, the

owner wants to know what is the 99% upper bound that can be let out. Please interpret your result.

(1 pt.) e) Why is the upper limit from part b) different from the upper bound in part d)? Please explain your answer using the symbols that are different and why different symbols are used.

Additional Problems: 8.31, 8.33, 8.35, 8.39 Practice Problems: 8.55 (p.360), 8.57 (p.360), 8.59 (p.360)

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STAT 350 (Spring 2017) Homework 7 (20 points) 2

(4 pts.) 3. Some municipal managers complain a city bus route is the most difficult service to fulfill. Traffic jams and roadwork are often the cause of unreliable service. In an effort to analyze current city bus transportation in Atlanta, Georgia, a random sample of 19 routes and stops was obtained. The number of minutes the bus was late (compared with the posted route times) was recorded. The sample mean was 8.5 minutes with a sample standard deviation of 3.75 minutes. There were some buses who arrived on time (a value of 0.00), however, no busses arrived early. Assume the underlying distribution of late times is normal.

(2 pts.) a) Find a 95% confidence interval for the true mean number of minutes a city bus in

Atlanta is late. Please interpret your answer. (1 pts.) b) If city buses in Atlanta consistently arrive more than ten minutes late, the mayor

receives a large number of phone calls from irate citizens. Using your answer to part (a), is there any evidence at the 95% significance level to suggest the mayor will be receiving nasty phone calls? Justify your answer. Hint: Think about the size of the standard error.

(1 pt.) c) Determine the number of routes and stops that need to be sampled to ensure that the half-width of the interval in a) is at most 0.75 minute.

Additional Problems: 8.71, 8.75 Practice Problems: 9.1 (p.395), 9.3 (p.395), 9.5 (p.395), 9.33 (p.401), 9.35 (p.401) In the following problems, 'in context' means that you have to use the situation presented in the

problem. Answers of 'reject the null hypothesis' and 'fail to reject the null hypothesis' will receive no credit.

(5 pts.) 4. The College Board reported that the mean cumulative SAT score (Critical Reading,

Mathematics, and Writing) for 2013 college-bound seniors was 1498. Officials from the Pennsylvania State K – 12 schools would like to know whether their students have a mean cumulative SAT score less than 1498. If the mean score is too low, the students will have problems getting into college. Therefore, the school would need to invest a lot more money and resources into identifying and fixing the problems in the school system. A random sample of students from across the system is obtained, each cumulative SAT score is recorded, and the mean cumulative score is recorded.

(1 pt.) a) State the null and alternative hypotheses. (1 pt.) b) In context, explain what the Type I error is. (1 pt.) c) In context, explain what the Type II error is. (1 pt.) d) Which one is worse for the high school officials, Type I error or Type II error? Why? (1 pt.) e) Which one is worse for the students, Type I error or Type II error? Why? (4 pts.) 5. The stereotypical video-game player is a male teenager. However, recent studies

suggest that at least 45% of all players are women. A software company has decided to develop and market a sophisticated stock-market video game if the mean age of all video- game players is greater than 25. A random sample of players will be obtained, and the resulting data will be used to test the relevant hypothesis.

(1 pt.) a) State the null and alternative hypotheses. (1 pt.) b) In context, explain what the Type I error is. (1 pt.) c) In context, explain what the Type II error is. (1 pt.) d) Which one is worse for the software company, Type I error or Type II error? Why?

STAT 350 (Spring 2017) Homework 7 (20 points) 3

Additional Problems: 9.15, 9.19, 9.23, 9.25, 9.27, 9.29, 9.31, 9.43, 9.45, 9.47, 9.49