# STAT 200 Final Exam (Fall 2015)

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 hand-held calculators to aid in your

calculation, please cite the sources and explain how you get the results.

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1.

True or False. Justify

for full credit.

(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 .gif”>

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(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 < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level
of significance .
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Refer to the following frequency

distribution for Questions 2, 3, 4, and 5. Show

all work. Just the answer, without supporting work, will receive no credit.

The frequency distribution below shows the distribution for checkout

time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday

afternoon.

Checkout

Time (in minutes)

Frequency

Relative Frequency

1.0 – 1.9

3

2.0 – 2.9

12

3.0 – 3.9

0.20

4.0 – 4.9

3

5.0 -5.9

Total

25

2.

Complete the frequency table with frequency and

relative frequency. Express the relative frequency to two decimal places.

3.

What percentage of the checkout times was at least

3 minutes?

4.

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

5.

Does this distribution have positive skew or

negative skew? Why?

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Refer to the following

information for Questions 6 and 7. Show all work. Just the answer, without

supporting work, will receive no credit.

Consider selecting one card at a time from a 52-card deck. (Note: There are 4 aces in a deck of cards)

6.

If the card selection is without replacement, what

is the probability that the first card is an ace and the second card is also an

ace? (Express the answer in simplest

fraction form) (5

pts)

7.

If the card selection is with replacement, what is

the probability that the first card is an ace and

the second card is also an

ace? (Express the answer in simplest

fraction form)

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Refer to the following situation for Questions 8, 9, and

10.

The five-number summary below shows the grade distribution of two STAT

200 quizzes for a sample of 500 students.

Minimum

Q1

Median

Q3

Maximum

Quiz 1

15

45

55

85

100

Quiz 2

20

35

50

90

100

For

each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have

the same value requested; (d) It is impossible to tell using only the given

information. Then

explain your answer in each case.

8.

Which quiz has less interquartile range in grade

distribution?

9.

Which quiz has the greater percentage of students

with grades 90 and over?

10.

Which quiz has a greater percentage of students

with grades less than 60?

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Refer to the following

information for Questions 11, 12, and 13. Show

all work. Just the answer, without supporting work, will receive no credit.

There are 1000 students in a high school. Among the 1000 students, 800 students have a

laptop, and 300 students have a tablet.

150 students have both devices.

11.

What is the probability that a randomly selected

student has neither device?

12.

What is the probability that a randomly selected

student has a laptop, given that he/she

has a

tablet?

13.

Let event A be the selected student having a

laptop, and event B be the selected student having a tablet. Are A and B

independent events? Why or why not? .gif”>

14.

A combination lock uses three distinctive numbers

between 0 and 49 inclusive. How many

different ways can a sequence of three numbers be selected? (Show work)

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15.

Let random variable x represent the number of heads when a fair coin is tossed three

times. Show all work. Just the answer, without supporting work, will receive

no credit.

(a)

Construct a table describing the probability

distribution.

(b)

Determine the mean and standard deviation of x. (Round the answer to two decimal

places)

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16. Mimi just started her tennis class

three weeks ago. On average, she is able to return 20% of her opponent’s

serves. Assume her opponent serves 10

times.

(a)

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?

(b)

Find the probability that that she returns at least 1

of the 10 serves from her opponent.

(Show work)

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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 lengths of mature jalapeño fruits are normally distributed with a

mean of 3 inches and a standard deviation of 1 inch.

17.

What is the probability that a randomly selected

mature jalapeño fruit is between 1.5 and 4 inches long? (5 pts)

18.

Find the 90th percentile of the jalapeño

fruit length distribution.

19.

If a random sample of 100 mature jalapeño fruits is

selected, what is the standard deviation of the sample mean?

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20.

Arandom sample of 100 light bulbs has a mean

lifetime of 3000 hours. Assume that the population standard deviation of the

lifetime is 500 hours. Construct a 95% confidence interval

estimate of the mean lifetime. Show all work. Just the answer, without

supporting work, will

receive no credit.

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21. Consider the

hypothesis test given by

H0:p?0.5

H1:p?0.5

In a random

sample of 100 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.

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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 8

5

9 8

Assume we want to

use a 0.01 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.

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23.

The UMUC MiniMart sells four different types of

Halloween candy bags. The manager

reports that the four types are equally popular. Suppose that a sample of 500 purchases yields

observed counts 150, 110, 130, and 110 for types 1, 2, 3, and 4,

respectively.

Type

1

2

3

4

Number of Bags

150

110

130

110

Assume we want to use a 0.10

significance level to test the claim that the four 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.

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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

3

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.

(b)

Based on the equation from part (a), what is the

predicted value of y if x = 4?

Show all

work and justify your answer.

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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:

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Her null hypothesis and alternative hypothesis are:

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(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.