Statistics

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STAT 200 Introduction to Statistics

Name______________________________

Final Examination: Summer 20

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OL2 Instructor __________________________

Answer Sheet

Instructions:

This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.

Record your answers and work in this document.

Answer all 20 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 calculators, programs or software packages without explanation will not be accepted. If you need to use technology to aid in your calculation, you have to cite the source and explain how you get the results. For example, state the Excel function along with the required parameters when using Excel; describe the detailed steps when using a hand-held calculator; or provide the URL and detailed steps when using an online calculator, and so on.

Show all supporting work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.

You must complete the exam individually. Neither collaboration nor consultation with others is allowed. It is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others. Your exam will receive a zero grade unless you complete the following honor statement.

Please sign (or type) your name below the following honor statement:

I understand that it is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others. I promise that I did not discuss any aspect of this exam with anyone other than my instructor. I further promise that I neither gave nor received any unauthorized assistance on this exam, and that the work presented herein is entirely my own.

Name _____________________ Date___________________

Record your answers and work.

Answer:
(a)
(b)

Answer:
(a)

(b)

Problem Number	Solution
1	Answer: (a) (b)
2		Answer: (a) (b)
3	Answer: (a) (b) Justification for (a) and (b):
4
5	Answer: (a) Season Rainfall (in Inches) Frequency Cumulative Relative Frequency 0 – 9 .99 1 10 – 19 .99 22 20 – 29.99 0.84 30 – 30.99 0.98 40 – 40.99 1.00 Total 50 (b) (c) Work for (a) and (b):
6	Answer: (a) (b) Work for (a) and (b):
7	Answer: (a) (b) Work for (a):
8	Answer: (a) (b) Work for (a):
9	Answer: (a) (b) Work for (a) and (b):
10	Answer: (a) n = , p = , and q = . (b) Work for (b):
11	Answer: (a) (b) Work for (a) and (b):
12	Answer: (a) (b) Work for (a) and (b):
13	Answer: (a) (b) (c) (d) (e) (f) Work for (c) and (d):
14	Answer: (a) (b) Work for (a):
15	Answer: (a) (b) Work for (a):
16	Answer: (a) (b) (c) (d) (e) (f) (g) Work for (d) and (e):
17		Answer: (a) (b)
18
19	Answers: (a) (b) (c) (d) (e) (f) Work for (c) and (d):
20	Answer: (a) (b) (c) (d) Work for (a), (b) and (c):

STAT200: Introduction to Statistics

Final Examination, Summer 2018 OL

2

Page 1 of 8

STAT 200

OL2 Sections

Final Exam

Summer 2018

The final exam will be posted at 12:01 am on July 27, 2018, and it

is due at 11:59 pm on July 29, 2018 Eastern Time.

This is an open-book exam. You may refer to your text and other course materials

for the current course as you work on the exam, and you may use a calculator,

applets, or Excel. You must complete the exam individually. Neither collaboration

nor consultation with others is allowed. It is a violation of the UMUC Academic

Dishonesty and Plagiarism policy to use unauthorized materials or work from

others.

Answer all 20 questions. Make sure your answers are as complete as possible,

particularly when it asks for you to show your work. Answers that come straight

from calculators, programs or software packages without any explanation will not

be accepted. If you need to use technology (for example, Excel, online or hand-

held calculators, statistical packages) to aid in your calculation, you must cite the

sources and explain how you get the results. For example, state the Excel function

along with the required parameters when using Excel; describe the detailed steps

when using a hand-held calculator; or provide the URL and detailed steps when

using an online calculator, and so on.

Record your answers and work on the separate answer sheet provided.

This exam has 20 problems; 5% for each problems.

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.

STAT 200: Introduction to Statistics
Final Examination, Summer 2018 OL2

Page 2 of 8

1. Research has suggested that breakfast is the most important meal of the day. A nutritionist randomly

selects 100 individuals and asks them: “Did you have breakfast this morning? Yes or no?”

(a) What is an appropriate method for graphing the data?

(b) Why is it appropriate?

2. A pet store owner is interested in the number of pets owned by her customers. She takes a random

sample of 100 customers and asks them: “How many pets do you own?”

(a) What is an appropriate method for graphing the data?
(b) Why is it appropriate?

3. Choose the best answer. Justify for full

credit.

(a) The Knot.com surveyed nearly 13,000 couples, who married in 2017, and asked how much they

spent on their wedding. The average amount of money spent on was $33,391. The value $33,39

1

is a:

(i) parameter

(ii) statistic

(iii) cannot be determined from information provided.

(b) A marketing agent asked people to rank the quality of a new soap on a scale from

1 (poor) to 5 (excellent). The level of this measurement is

(i) nominal

(ii) ordinal

(iii) interval

(iv) ratio

4. A school district wanted to assess the effectiveness of a new reading readiness program for 1st

graders. The school district is divided into the individual first grade classrooms and 10

classrooms are randomly selected. All of the children in each of the 10 selected classrooms are

assessed.

(a) What type of sampling method is being used?
(b) Please explain your answer.

STAT 200: Introduction to Statistics
Final Examination, Summer 2018 OL2

Page 3 of 8

5. The frequency distribution below shows the distribution of average seasonal rainfall in San Francisco,

as measured in inches, for the years 1967-2017. (Show all work. Just the answer, without supporting

work, will receive no credit.)

Season Rainfall (in

Inches)

Frequency

Cumulative Relative

Frequency

0 – 9.99 1

10 – 19.99 22

20 – 29.99

0.8

4

30 – 30.99

0.98

40 – 40.99

1.00

Total 50

(a) Complete the frequency table with frequency and cumulative relative frequency. Express the
cumulative relative frequency to two decimal places.

(b) What percentage of season in this sample has a seasonal rainfall between 30 and 40.99 inches,
inclusive?

(c) Which of the following seasonal rainfall groups does the median of this distribution belong to?

10-19.99, 20 – 29.99, or 30 – 39.99? Why?

6. Consider selecting one card at a time from a 52-card deck. What is the probability that the first

card is a diamond and the second card is also a diamond? Express the probability in fraction

format. (Note: There are 13 diamonds in a deck of cards) (Show all work. Just the answer, without

supporting work, will receive no credit.)

(a) Assuming the card selection is without replacement.

(b) Assuming the card selection is with replacement.

7. Mimi has seven new summer outfits. She plans to pack three of the new summer outfits in her

trip to Tokyo.

(a) How many different ways can the three summer outfits be selected?

(b) Please describe the method used and the reason why it is appropriate for answering the

question.

Just the answer, without the description and reason, will receive no credit.

8. A businessman needs to visit clients in 5 different cities.

(a) How many different routes can he take?

(b) Please describe the method used and the reason why it is appropriate for answering the question.

Just the answer, without the description and reason, will receive no credit.

STAT 200: Introduction to Statistics
Final Examination, Summer 2018 OL2

Page 4 of 8

9. Recent research suggests that car ownership may have peaked. The following probability

distribution table shows the random variable, x, where x is number of cars owned by household:

x P(x)

0 0.10

1 0.19

2 0.4

5

3 0.22

4 0.04

(a) Determine the mean of x (Round the answer to two decimal places). Show all work. Answers

without supporting work will not receive credit.

(b) Determine the standard deviation of x. (Round the answer to two decimal places) Show all
work. Answers without supporting work will not receive credit.

10. Max Scherzer, the starting pitcher for the Nationals, on average, has a 0.250 probability of hitting

the ball in a single “at bat”. In one game, he gets 6 “at bats.”

(a) Let X be the number of hits that Max 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 he gets at least 4 hits in the one game. (Round the answer to

3

decimal places) Show all work. Just the answer, without supporting work, will receive no

credit.

11. Assume that gas mileage for cars is normally distributed with a mean of 23.5 miles

per gallon and a standard deviation of 10 miles per gallon. Show all work. Just the

answer, without supporting work, will receive no credit.

(a) What is the probability that a randomly selected car gets between 20 and 25 miles per gallon?

(Round the answer to 4 decimal places)

(b) Find the 80th percentile of the miles per gallon distribution. (Round the answer to 2 decimal
places)

STAT 200: Introduction to Statistics
Final Examination, Summer 2018 OL2

Page 5 of 8

12. Based on the performance of all individuals who tested between July 1, 2013 and June 30,

2016, the GRE Verbal Reasoning scores are normally distributed with a mean of 149.97 and a

standard deviation of 8.49. (https://www.ets.org/s/gre/pdf/gre_guide_table1a ). Show all

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

(a) For a sample of size 64, state the standard deviation of the sample mean (the “standard error of

the mean”). (Round your answer to three decimal places)

(b) Suppose a sample of size 64 is taken. Find the probability that the sample mean GRE Verbal

Reasoning scores is more than 152. (Round your answer to three decimal places)

13. The color distribution of plain M&M’s varies by the factory in which they were made. The

Hackettstown, New Jersey plant uses the following color distribution for plain M&M’s: 12.5%

red, 25% orange, 12.5% yellow, 12.5% green, 25% blue, and 12.5% brown. Each piece of candy

in a random sample of 100 plain M&M’s from the Hackettstown factory was classified according

to color, and the results are listed below. Use a 0.05 significance level to test the claim that the

Hackettstown factory color distribution is correct. Describe method used for calculating answer.

Color Red Orange Yellow Green Blue Brown

Number 11 28 20 9 20 12

(a) Identify the appropriate hypothesis test and explain the reasons why it is appropriate for analyzing
this data.

(b) Identify the null hypothesis and the alternative hypothesis.
(c) Determine the test statistic. (Round your answer to two decimal places)
(d) Determine the p-value. (Round your answer to two decimal places)
(e) Compare p-value and significance level α. What decision should be made regarding the null

hypothesis (e.g., reject or fail to reject) and why?

(f) Is there sufficient evidence to support the claim that the Hackettstown factory color distribution is
correct? Justify your answer.

14. A survey showed that 680 of the 1000 adult respondents believe in global warming.

(a) Construct a 95% confidence interval estimate of the proportion of adults believing in global

warming. (Round the lower bound and upper bound of the confidence interval to three decimal

places)

Include description of how confidence interval was constructed.

(b) Describe the results of the survey in everyday language.

STAT 200: Introduction to Statistics
Final Examination, Summer 2018 OL2

Page 6 of 8

15. In a study to assess the effectiveness of garlic for lowering cholesterol, 60 adults were treated with

garlic tablets. Cholesterol levels were measured before and after treatment. The changes in their LDL

cholesterol (in mg/dL) have a mean of 7 and a standard deviation of 4.

(a) Construct a 90% interval estimate of the mean change in LDL cholesterol after the garlic tablet

treatment. (Round the lower bound and upper bound of the confidence interval to two decimal places)

Include description of how confidence interval was constructed.

(b) Describe the results of the study in everyday language.

16. A health educator was interested in determining whether college students at her college really do gain

weigh during their freshman year. A random sample of 5 college students was chosen and the weight

for each student was recorded in August and May. Does the data below suggest that college students

gain weight during their freshman year? The health educator wants to use a 0.05 significance

level to test the claim.

Weight (pounds)

Student August May

1
2
3
4
5

175 180

170 164

135 142

160 166

200 208

(a) What is the appropriate hypothesis test to use for this analysis? Please identify and explain why

it is appropriate.

(b) Let μ1 = mean weight in May. Let μ2 = mean weight in August. Which of the following
statements correctly defines the null hypothesis?

(i) μ1 – μ2 > 0 (μd > 0)
(ii) μ1 – μ2 = 0 (μd = 0)
(iii) μ1 – μ2 < 0 (μd < 0)

(c) Let μ1 = mean weight in May. Let μ2 = mean weight in August. Which of the following
statements correctly defines the alternative hypothesis?

(i) μ1 – μ2 > 0 (μd > 0)
(ii) μ1 – μ2 = 0 (μd = 0)
(iii) μ1 – μ2 < 0 (μd < 0)

(d) Determine the test statistic. Round your answer to three decimal places. Describe method used
for obtaining the test statistic.

(e) Determine the p-value. Round your answer to three decimal places. Describe method used for
obtaining the p-value.

(f) Compare p-value and significance level α. What decision should be made regarding the null
hypothesis (e.g., reject or fail to reject) and why?

(g) What do the results of this study tell us about freshman college student weight gain? Justify your
conclusion.

STAT 200: Introduction to Statistics
Final Examination, Summer 2018 OL2

Page 7 of 8

17. A psychologist is interested in studying the effectiveness of different therapies for depression. The

psychologist selects 90 clients and randomly assigns thirty to each of the following groups:

cognitive-behavioral treatment, psychodynamic psychotherapy, or client-centered treatment. The

dependent measure is a score on a depression inventory after 4 weeks of treatment. The psychologist

wants to test the claim that all three therapies are equally effective in reducing symptoms of

depression.

(a) Which statistical approach should be used?

i. confidence interval

ii. t-test

iii. ANOVA

iv. Chi square

(b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate

statistical approach?

18. A study was conducted to see whether monetary incentives to use less water during times of drought

had an effect on water usage. Sixty single family homeowners were randomly assigned to one of two

groups: 1) monetary incentives and 2) no monetary incentives. At the end of three months, the total

amount of water usage for each household, in gallons, was measured.

(a) What would be the appropriate hypothesis test to use to test the claim that monetary incentives

reduce water usage?

i. t-test for two independent samples

ii. t-test for dependent samples

iii. z-test for population mean

iv. correlation

(b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate
statistical approach?

STAT 200: Introduction to Statistics
Final Examination, Summer 2018 OL2

Page 8 of 8

19. A researcher claims the proportion of auto accidents that involve teenage drivers is less than 20%.

ABC Insurance Company checks police records on 400 randomly selected auto accidents and notes

that teenagers were at the wheel in 64 of them. Assume the company wants to use a 0.05

significance level to test the researcher’s claim.

(a) What is the appropriate hypothesis test to use for this analysis? Please identify and explain
why it is appropriate.

(b) Identify the null hypothesis and the alternative hypothesis.
(c) Determine the test statistic. Round your answer to two decimal places. Describe method used

for obtaining the test statistic

(d) Determine the p-value. Round your answer to three decimal places. Describe method used for
obtaining the p-value

(e) Compare p-value and significance level α. What decision should be made regarding the null
hypothesis (e.g., reject or fail to reject) and why?

(f) Is there sufficient evidence to support the researcher’s claim that the proportion of auto
accidents that involve teenage drivers is less than 20%? Explain your conclusion.

20. A business analyst believes that December holiday sales in 2016 are a good predictor of December

holiday sales in 2017. A random sample of 8 toys stores produced the following data where x is the

amount of December holiday sales in 2016 and y is the amount of December sales in 2017, in dollars.

x y

10257 11689

6556 6438

7224 8662

9987 9454

11568 12004

8453 8231

4235 5048

5576 4850

(a) Find an equation of the least squares regression line. Round the slope and y-intercept
value to two decimal places. Describe method for obtaining results.

(b) Based on the equation from part (a), what is the predicted 2017 December holiday sales if the 2016
December holiday sales is 6,000 dollars? Show all work and justify your answer.

(c) Based on the equation from part (a), what is the predicted 2017 December holiday sales if the 2016
December holiday sales is 20,000 dollars? Show all work and justify your answer.

(d) Which predicted 2017 holiday sales that you calculated for (b) and (c) do you think is closer to
the true 2017 holiday sales and why?