Assignment:
Q1. Mimi was the 5th seed in 2012 UMUC Tennis Open that took place in August. In this tournament, she won 83 of her 100 serving games. Based on UMUC Sports Network, she wins 80% of the serving games in her 5-year tennis career.
(a) Find a 95% confidence interval estimate of the proportion of serving games Mimi won.
(b) 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.
(c) A sport reporter commented that Mimi's performance in the tournament is better than usual. You decide to test if the reporter's claim is valid by using hypothesis testing that you just learned from STAT 200 class. What are your null and alternative hypotheses?
(d) What is the test statistic?
(e) What is the P-value?
(f) What is the critical value?
(g) What is your conclusion of the testing at 0.05 significance level? Why?
Q2. A simple random sample of 120 SAT scores has a mean of 1540. Assume that SAT scores have a population standard deviation of 333.
(a) Construct a 95% confidence interval estimate of the mean SAT score.
(b) Is a 99% 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 99% confidence interval]
Q3. The playing times of songs are normally distributed. Listed below are the playing times (in seconds) of 10 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.
448 231 246 246 227 213 239 258 255 257
(a) What are your null hypothesis and alternative hypothesis?
(b) What is the test statistic?
(c) What is your conclusion? Why?