# Statistics

August 30, 2017

Question
· Make sure your answers are as complete as possible and show your work/argument. When there are calculations involved, you should show how you come up with your answers with critical work and/or necessary tables. You must show why you choose certain answer for true-or-false and multiple choice questions.Answers that come straight from program software packages will not be accepted.

1. (2 pts) True or False: In a right-tailed test, the test statistic is 1.5. If we know P(X

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(a) (2 pts) Find the test statistic. (Show work and round the answer to two decimal places)

(b)(2 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 .gif”>at the.gif”>level? Explain.

7. (5 points) The SAT scores are normally distributed. A simple random sample of100 SAT scores has a sample mean of 1500 anda samplestandard deviation of 300.

(a) (1 pt) What distribution will you use to determine the critical value for a confidence interval estimate of the mean SAT score? Why?

(b) (3 pts) Construct a 95% confidence interval estimate of the mean SAT score.(Show work and round the answer to two decimal places)

(c) (1 pt) Is a 99% confidence interval estimate of the mean SAT score wider than the 95% confidence interval estimate you got from part (b)? Why? [You don’t have to construct the 99% confidence interval]

8. (6 pts) Assume the population is normally distributed with population standard deviation of 100.Given a sample size of 25, with sample mean 770, we perform the following hypothesis test.

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(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)

(c) (2 pts) What is the p-value? (Show workand round the answer to two decimal places)

(d) (1 pts) What is your conclusion of the test at the ? = 0.10 level? Why? (Show work)

9. (7 points) Consider the hypothesis test given by

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Assume the population is normally distributed. In a random sample of25 subjects, the sample mean is found to be.gif”>, and the sample standard deviation is.gif”>

(a)(1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?

(b) (1 pt) Is the test a right-tailed, left-tailed or two-tailed test?

(c) (2 pts) Find the test statistic. (Show work and round the answer to two decimal places)

(d)(2 pts) Determine the P-value for this test. (Show work and round the answer to three decimal places)

(e)(1 pt) Is there sufficient evidence to justify the rejection of .gif”>at the.gif”>level? Explain.

10. (7 pts) A new prep class was designed to improve SAT math test scores. Five students were selected at random. Their scores on two practice exams were recorded; one before the class and one after. The data recorded in the table below. We want to test if the scores, on average, are higher after the class.

SAT Math Score

Student 1

Student 2

Student 3

Student 4

Student 5

Score before the class

620

700

650

640

620

Score after the class

640

700

670

670

630

(a) (1 pt) 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) (1 pt) Let?d be the population mean for the differences of scores (scores after the class –before the class). Fill in the correct symbol (=,?, ?, >, ?, <) for the null and alternative hypotheses.

(i) H0: ?d ________ 0

(ii) Ha: ?d ________ 0

(c) (2 pts) What is the test statistic? (Show work andround the answer to three decimal places)

(d) (2 pts) What is the p-value? (Show workand round the answer to three decimal places)

(e) (1 pt)What is your conclusion of the test at the ? = 0.05 level? Why? (Show work)

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