In a two-tailed test, the test statistic is 1.5. In addition, we know P(T < 1.5) = 0.96.

1. What is the p-value for this test? (Justify for full credit) (a) 0.96

(b) 1.92

(c) 0.04

(d) 0.08

2. What is your conclusion for the test? (Justify for full credit)

(a) Reject null hypothesis

(b) Fail to reject null hypothesis

(c) Cannot be determined

3. True or False: If a 95% confidence interval contains 1, then the 99% confidence interval for the same parameter must contain 1. (Justify for full credit)

4. Three hundred students took a chemistry test. You sampled 50 students to estimate the average score and the standard deviation. How many degrees of freedom were there in the estimation of the standard deviation? (Justify for full credit)

a. 50

b. 49

c. 300

d. 299

For Questions 5 & 6- Mimi was the 5th seed in 2015 UMUC Tennis Open that took place in August.  In this tournament, she won 90 of her 100 serving games.

5. Find a 95% confidence interval estimate of the proportion of serving games Mimi won. (Explain how you get the critical value, show work and round the answer to three decimal places)

6. According to UMUC Sports Network, Mimi wins 85% of the serving games in her 5- year tennis career. In order to determine if this tournament result is better than her career record of 85%.  We would like to perform the following hypothesis test:

H₀: p = 0.85

H_a: p > 0.85

(a) Find the test statistic. (Show work and round the answer to two decimal places)

(b) Determine the P-value for this test. (Show work and round the answer to three decimal places. If you use technology to find the P-value, you have to describe the steps)

(c) Is there sufficient evidence to justify the rejection of H₀ at the α = 0.05 level? Explain

7. The SAT scores are normally distributed. A simple random sample of 100 SAT scores has a sample mean of 1500 and a sample standard deviation of 300.

(a) What distribution will you use to determine the critical value for a confidence interval estimate of the mean SAT score? Why?

(b) Construct a 90% confidence interval estimate of the mean SAT score. (Show work and round the answer to two decimal places)

(c) Is a 95% confidence interval estimate of the mean SAT score wider than the 90% confidence interval estimate you got from part (b)? Why? [You don't have to construct the 95% confidence interval]

8. Assume the population is normally distributed with population standard deviation of 100. Given a sample size of 25, with sample mean 720, we perform the following hypothesis test.

H₀: μ = 750          

H_a: μ < 750

(a) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?

(b) What is the test statistic? (Show work and round the answer to three decimal places)

(c) What is the p-value? (Show work and round the answer to two decimal places. If you use technology to find the P-value, you have to describe the steps)

(d) What is your conclusion of the test at the α = 0.10 level? Why? (Show work)

9. Consider the hypothesis test given by

H₀: μ = 650          

H_a: μ > 650

Assume the population is normally distributed. In a random sample of 64 subjects, the sample mean is found to be x^- = 655, and the sample standard deviation is       

(a) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?

(b) Is the test a right-tailed, left-tailed or two-tailed test?

(c) Find the test statistic. (Show work and round the answer to two decimal places)

(d) Determine the P-value for this test. (Show work and round the answer to three decimal places if necessary. If you use technology to find the P-value, you have to describe the steps)

(e) Is there sufficient evidence to justify the rejection of H₀ at the α = 0.05 level? Explain.

10. A company claims that its new 3-month diet program is effective in weight loss. Five people on the program were selected at random. Their weights before and after the 3-month program were recorded. The data are recorded in the table below. We want to test if the weights, on average, are less after the program.

(a) Which of the following is the appropriate test and best distribution to use for the test?

(i) Two independent means, normal distribution

(ii) Two independent means, Student's t-distribution

(iii) Matched or paired samples, normal distribution

(iv) Matched or paired samples, Student's t-distribution

(b) Let μ_d be the population mean for the differences of weights (weight after the program - before the program). Fill in the correct symbol (=, ≠, ≥, >, ≤, <) for the null and alternative hypotheses.

(i) H₀: μ_d ______ 0

(ii) H_a: μ_d_____ 0

(c) What is the test statistic? (Show work and round the answer to three decimal places)

(d) What is the p-value? (Show work and round the answer to three decimal places)

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