## STAT 200 QUIZ 3 In a right-tailed test, the test statistic

Question

STAT 200 QUIZ 3

Section 7655 Summer 2016

I have completed this assignment myself, working independently and not consulting

anyone except the instructor.

NAME_____________________________

INSTRUCTIONS

The quiz is worth 50 points total.

The quiz covers Week 5 and 6 materials.

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.

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 Wednesday, August 3. 2016.

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

0.96, then we reject the null hypothesis at 0.05 level of significance. (Justify for full credit)

2. (2 pts) True or False: If a 99% confidence interval contains 1, then the 95% confidence

interval for the same parameter must contain 1. (Justify for full credit)

3. (2 pts) Which of the following could reduce the rate of Type I error? (Justify for full credit)

a. Making the significant level from 0.01 to 0.05

b. Making the significant level from 0.05 to 0.01

c. Increase the ? level

d. Increase the power

4. (2 pts) 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)

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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 75 of her 100 serving games.

5. (2 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)

6. (5 pts) According to UMUC Sports Network, Mimi wins 80% of the serving games in her 5year tennis career. In order to determine if this tournament result is worse than her career record

of 80%. We would like to perform the following hypothesis test:

H 0 : p=0. 80

H a : p< 0.80

(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)

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(c) (1 pt) Is there sufficient evidence to justify the rejection of

H0

at the

? =0.05

level?

Explain.

7. (5 points) 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) (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]

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8. (10 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.

H 0 : ?=750

H a : ?> 750

(a) (2 pts) Is this test for population proportion, mean or standard deviation? What

distribution should you apply for the critical value?

(b) (3 pts) What is the test statistic? (Show work and round the answer to three decimal

places)

(c) (3 pts) What is the p-value? (Show work and round the answer to two decimal places)

(d) (2 pts) What is your conclusion of the test at the ? = 0.10 level? Why? (Show work)

9. (10 points) Consider the hypothesis test given by

H 0 : ?=650

H a : ?> 650

Assume the population is normally distributed. In a random sample of 25 subjects, the sample

mean is found to be ´x =655 , and the sample standard deviation is s=28.

(a) (2 pts) Is this test for population proportion, mean or standard deviation? What

distribution should you apply for the critical value?

4

(b) (2 pts) 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) (2 pt) Is there sufficient evidence to justify the rejection of

H0

at the

? =0.02

level?

Explain.

10. (10 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

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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) (2 pts) 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) (2 pts) 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 and round the answer to three decimal places)

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

(e) (2 pts) What is your conclusion of the test at the ? = 0.05 level? Why? (Show work)

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