STAT 200 QUIZ 3 Section Fall 2016 I have completed this assignment myself, working independently and not consulting anyone except the instructor. NAME_____________________________ INSTRUCTIONS The quiz is worth 40 points total. The quiz covers week 6 Make sure your answers are as complete as possible and show your work/argument. In particular, when there are calculations involved, you should show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from program software packages will not be accepted. The quiz is open book and open notes. This means that you may refer to your textbook, notes, and online course materials, but you must work independently and may not consult anyone. The brief honor statement is on top of the exam. If you fail to put your name under the statement, your quiz will not be accepted. You may take as much time as you wish, provided you turn in your quiz via LEO by 11:59 pm EDT on Sunday, December 11, 2016. 1. (4 points) An important component in the evaluating confidence interval and performing hypothesis test is the critical value, and the critical value depends on what distribution we should apply. Please fill in the corresponding distribution in the following table. Distribution for the Critical Value Parameter Requirements Proportion p (1) simple random sample (2) conditions for the binomial distribution are satisfied (3) np >= 5 and nq >= 5 Mean (1) simple random sample (2) the population is normally distributed or n > 30 (3) population standard deviation is unknown Mean (1) simple random sample (2) the population is normally distributed or n > 30 (3) population standard deviation is known Standard deviation (1) simple random sample (2) the population is normally distributed 1 2. (15 points) Mimi was the 5th seed in 2014 UMUC Tennis Open that took place in August. In this tournament, she won 75 of her 100 serving games. Based on UMUC Sports Network, she wins 80% of the serving games in her 5-year tennis career. (a) (3 pts) Find a 90% confidence interval estimate of the proportion of serving games Mimi won. (Show work and round the answer to three decimal places) (b) (2 pts) Based on the confidence interval estimate you got in part (a), is this tournament result consistent with her career record of 80%? Why or why not? Please explain your conclusion. Parts (c) through (g): A sport reporter commented that Mimi's performance in the tournament is worse than her career average of 80%. You decide to test if the reporter's claim is valid by using hypothesis testing that you just learned from STAT 200 class. (c) (2 pts) What are your null and alternative hypotheses? (d) (2 pts) What is the test statistic? (Show work and round the answer to two decimal places) 2 (e) (2 pts) What is the P-value? (Show work and express the answer in four decimal places) (f) (2 pts) What is the critical value if you perform the test at 0.10 significance level? (Show work) (g) (2 pts) What is your conclusion of the testing at 0.10 significance level? Why? 3. (5 points) A simple random sample of 120 SAT scores has a sample mean of 1540. Assume that SAT scores have a population standard deviation of 300. (a) (4 pts) Construct a 95% confidence interval estimate of the mean SAT score. (Show work and round the answer to two decimal places) (b) (1 pt) Is a 90% confidence interval estimate of the mean SAT score wider than the 95% confidence interval estimate you got from part (a)? Why? [You don't have to construct the 90% confidence interval] 3 4. (5 points) Consider the hypothesis test given by H 0 : 670 H1 : 670. In a random sample of 70 subjects, the sample mean is found to be standard deviation is known to be x 680. The population 27. (a) (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value? (b) (3 pts) Determine the P-value for this test. (Show work and round the answer to three decimal places) (c) (1 pt) Is there sufficient evidence to justify the rejection of H0 at the 0.02 level? Explain. 5. (6 pts) The playing times of songs are normally distributed. Listed below are the playing times (in seconds) of 5 songs from a random sample. Use a 0.05 significance level to test the claim that the songs are from a population with a standard deviation less than 1 minute. 450 250 200 200 400 (a) (1 pt) What are your null hypothesis and alternative hypothesis? 4 (b) (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value? (c) (2 pts) What is the test statistic? (Show work and round the answer to two decimal places) (d) (2 pts) What is your conclusion? Why? (Show work) 6. (5 pts) Assume the population is normally distributed. Given a sample size of 25, with sample mean 740 and sample standard deviation 80, we perform the following hypothesis test. H 0 : 750 H1 : 750 (a) (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value? (b) (2 pts) What is the test statistic? (Show work and round the answer to three decimal places) 5 (c) (2 pts) What is your conclusion of the test at the = 0.10 level? Why? (Show work) 6