# UMUC Stat200 Winter 2015 Final Exam OL4/US2 latest 2015 december 13th

Question

Please look at the attachment for the Final Exam Questions. Some of the the symbols were not able to copy over from the exam. A sheet to input the answers is also attached. Thank you!

1.True or False. Justify for full credit. (15 pts)

(a)If the variance of a data set is zero, then all the observations in this data set are zero.

(b)If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.

(c) Assume X follows a continuous distribution which is symmetric about 0. If P(X>2) = 0.3, then P(X<-3) ?0.3

(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.

(e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a Student’s t-distribution with P(T 0.5

In a random sample of 625 subjects, the sample proportion is found to be pˆ=0.45.

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of H0 at the ??0.01 level?

Explain. (15 pts)

22.Consumption of large amounts of alcohol is known to increase reaction time. To investigate the effects of small amounts of alcohol, reaction time was recorded for five individuals before and after the consumption of 2 ounces of alcohol. Do the data below suggest that consumption of 2 ounces of alcohol increases mean reaction time?

Reaction Time (seconds)

Subject

Before After

1

6 7

2

8 8

3

4 6

4

7 9

5

9 8

Assume we want to use a 0.05 significance level to test the claim.

(a)Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that consumption of 2 ounces of alcohol increases mean reaction time? Justify your conclusion.

(15 pts)

23.The UMUC MiniMart sells four different types of coffee mugs. The manager reports that the five types are equally popular. Suppose that a sample of 500 purchases yields observed counts 120, 90, 110, 100, and 80 for types 1, 2, 3, 4, and 5 respectively.

Type

1

2

3

4

5

Number of Bags

120

90

110

100

80

Assume we want to use a 0.05 significance level to test the claim that the five types are equally popular.

(a) Identify the null hypothesis and the alternative hypothesis.

(b)Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value for the test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d)Is there sufficient evidence to support the manager’s claim that the four types are equally popular? Justify your answer.

(15 pts)

24. A random sample of 4 professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

x

0

1

3

5

y

1

2

5

8

(a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.(10 pts)

(b) Based on the equation from part (a), what is the predicted value of y if x = 2? Show all

work and justify your answer. (5 pts)

25.A STAT 200 instructor is interested in whether there is any variation in the final exam grades between her two classes Data collected from the two classes are as follows:

Her null hypothesis and alternative hypothesis are:

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

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

Explain.

(10 pts)

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