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?
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(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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