# STAT 200 QUIZ 3 Solutions

1. (15 points) Mimi was the 5th seed in 2012 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 95% confidence interval estimate of the proportion of serving games

Mimi won. (Show work)

(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.

(c) (2 pts) A sport reporter commented that Mimi’s performance in the tournament is worse 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) (2 pts) What is the test statistic? (Show work)

(e) (2 pts) What is the P-value? (Show work)

(f) (2 pts) What is the critical value? (Show work)

(g) (2 pts) What is your conclusion of the testing at 0.05 significance level? Why?

2. (6 points) A simple random sample of 120 SAT scores has a 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)

(b) (2 pts) 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]

3. (6 points) Consider the hypothesis test given by

H 0 : µ = 670

H1 : µ ≠ 670.

In a random sample of 70 subjects, the sample mean is found to be

population standard deviation is known to be σ = 27.

x = 678.2. The

(a) (4 pts) Determine the P-value for this test. (Show work)

(b) (2 pts) Is there sufficient evidence to justify the rejection of level? Explain.

H 0 at the α = 0.02

4. (7 pts) 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) (1 pts) What are your null hypothesis and alternative hypothesis?

(b) (4 pts) What is the test statistic? (Show work)

(c) (2 pts) What is your conclusion? Why? (Show work)

5. (6 pts) Assume the population is normally distributed. Given a sample size of 25, with sample mean 736.2 and sample standard deviation 82.3, we perform the

following hypothesis test.

H 0 : µ = 750

H1 : µ < 750

What is the conclusion of the test at the α = 0.10 level? Explain your answer. (Show work)

(a) (3 pts) Find a 95% confidence interval estimate of the proportion of serving games

Mimi won. (Show work)

(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.

(c) (2 pts) A sport reporter commented that Mimi’s performance in the tournament is worse 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) (2 pts) What is the test statistic? (Show work)

(e) (2 pts) What is the P-value? (Show work)

(f) (2 pts) What is the critical value? (Show work)

(g) (2 pts) What is your conclusion of the testing at 0.05 significance level? Why?

2. (6 points) A simple random sample of 120 SAT scores has a 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)

(b) (2 pts) 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]

3. (6 points) Consider the hypothesis test given by

H 0 : µ = 670

H1 : µ ≠ 670.

In a random sample of 70 subjects, the sample mean is found to be

population standard deviation is known to be σ = 27.

x = 678.2. The

(a) (4 pts) Determine the P-value for this test. (Show work)

(b) (2 pts) Is there sufficient evidence to justify the rejection of level? Explain.

H 0 at the α = 0.02

4. (7 pts) 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) (1 pts) What are your null hypothesis and alternative hypothesis?

(b) (4 pts) What is the test statistic? (Show work)

(c) (2 pts) What is your conclusion? Why? (Show work)

5. (6 pts) Assume the population is normally distributed. Given a sample size of 25, with sample mean 736.2 and sample standard deviation 82.3, we perform the

following hypothesis test.

H 0 : µ = 750

H1 : µ < 750

What is the conclusion of the test at the α = 0.10 level? Explain your answer. (Show work)

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