Answer all 25 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted. If you need to use software (for example, Excel) and /or online or handheld calculators to aid in your calculation, please cite the sources and explain how you get the results.
Record your answers and work on the separate answer sheet provided.
This exam has 250 total points.
You must include the Honor Pledge on the title page of your submitted final exam. Exams submitted without the Honor Pledge will not be accepted.
 If the variance from a data set is zero, then all the observations in this data set must be identical.
 The mean is always equal to the median for a normal distribution.
 A 99% confidence interval is wider than a 95% confidence interval of the same parameter.
 It is easier to reject the null hypothesis if we use a smaller significance level α.
Checkout Time (in minutes)

Frequency

Relative Frequency


1.0 – 1.9

4


2.0 – 2.9

0.4


3.0 – 3.9


4.0 – 4.9

5


Total

25


2.

Complete the frequency table with frequency and relative frequency.

(5 pts)


3.

What percentage of the checkout times was at least 3 minutes?

(5 pts)


4.

In what class interval must the median lie? Explain your answer.

(5 pts)

 Assume that the largest observation in this dataset is 4.8. Suppose this observation were incorrectly recorded as 8.4 instead of 4.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why? (5 pts)
 What is the probability that the outcome of the second roll is greater than 4, given that the first roll is an even number? (10 pts)
STAT 200: Introduction to Statistics Final Examination, Spring 2015 OL4/US2 
Page 3 of 6


8. 
Are A and B independent? Why or why not?

(5 pts)

Minimum

Q1

Median

Q3

Maximum


Quiz 1

12

40

60

95

100

Quiz 2

20

35

50

90

100

 Which quiz has less interquartile range in grade distribution?
 Which quiz has the greater percentage of students with grades 90 and over?
 Which quiz has a greater percentage of students with grades less than 60?
 What is the probability that a randomly selected junior is taking at least one of these two courses? (10 pts)
 What is the probability that a randomly selected junior is taking PSYC300, given that he/she is taking STAT200? (10 pts)
16. Mimi just started her tennis class three weeks ago. On average, she is able to return 30% of her opponent’s serves. Assume her opponent serves 10 times. Show all work. Just the answer, without supporting work, will receive no credit.
 Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial
probability distribution. What is the number of trials (n), probability of successes (p) and


probability of failures (q), respectively?

(5 pts)


(b) 
Find the probability that that she returns at least 1 of the 10 serves from her opponent.

(10 pts)

(c) 
How many serves can she expect to return?

(5 pts)

Refer to the following information for Questions 17, 18, and 19. Show all work. Just the answer, without supporting work, will receive no credit.
The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet.
 What is the probability that a randomly selected pecan tree is between 10 and 12 feet tall? (10 pts)
18. Find the 3^{rd} quartile of the pecan tree height distribution. (5 pts)
 If a random sample of 100 pecan trees is selected, what is the standard deviation of the samplemean? (5 pts)
20. A random sample of 225 SAT scores has a sample mean of 1500. Assume that SAT scores have a population standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores. Show all work. Just the answer, without supporting work, will receive
no credit. 
(10 pts)


21. 
Consider the hypothesis test given by


H _{0} : p

0.5


H_{1} : p

0.5


ˆ

0.53 .


In a random sample of 225 subjects, the sample proportion is found to be p

 Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
 Determine the pvalue for this test. Show all work; writing the correct Pvalue, without supporting work, will receive no credit.
 Consumption of a large amount 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 2 ounces of alcohol was consumed by each. Does the data below suggest that the 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

10

5

9

10

 Identify the null hypothesis and the alternative hypothesis.
 Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
 Determine the pvalue. Show all work; writing the correct critical value, without supporting work, will receive no credit.
 Is there sufficient evidence to support the claim that the consumption of 2 ounces of alcohol increases mean reaction time? Justify your conclusion.
23. 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:
 Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
 Determine the pvalue for this test. Show all work; writing the correct Pvalue, without supporting work, will receive no credit.
(c) Is there sufficient evidence to justify the rejection of H_{0} at the

0.01 level?

Explain.

(10 pts)

 Find an equation of the least squares regression line. Show all work; writing the correct
 Based on the equation from part (a), what is the predicted value of y if x = 4? Show all work and justify your answer. (5 pts)
 The UMUC Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer.
Color

Brown

Yellow

Orange

Green

Tan

Number

42

21

12

7

18

 Identify the null hypothesis and the alternative hypothesis.
 Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
 Determine the pvalue. Show all work; writing the correct critical value, without supporting work, will receive no credit.
 Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer.(15 pts)