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STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 1 of 10

STAT 200

OL4/US2 Sections

Final Exam

Fall 2018

The final exam will be posted at 12:01 am on December 14, and it is

due at 11:59 pm on December 16, 2018. Eastern Time is our

reference 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. 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.

Show all of your supporting work and reasoning. 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.

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

This exam has 20 questions; 5% for each question.

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, Fall 2018 OL4_US2 Page 2 of 10

1. The U.S. Census Bureau needs to estimate the median income of females in the U.S. They collect

incomes from 3500 females. Choose the best answer. Justify for full credit.

(a) Which of the followings is the parameter?

(i) Set of income responses from 3500 females in the US

(ii) Median Income of set of 3500 females in the US

(iii) Set of income responses from all females in the US

(iv) Median income of set of all females in the US

(b) Which of the followings is the sample?

(i) Set of income responses from 3500 females in the US

(ii) Median income of set of 3500 females in the US

(iii) Set of income responses from all females in the US

(iv) Median income of set of all females in the US

2. Choose the best answer. Justify for full credit.

(a) What type of data are student ID numbers considered?

(i) interval

(ii) nominal

(iii) ordinal

(iv) ratio

(b) The quality control department of a semiconductor manufacturing company tests every 100th

product from the assembly line. This type of sampling is called:

(i) cluster

(ii) convenience

(iii) systematic

(iv) stratified

STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 3 of 10

3. The midterm exam scores in a statistics class are shown in the following table:

67 92 76 45 85 70 87 84 67 72

84 85 55 76 84 98 59 93 87 83

(a) Complete the following frequency distribution table using 6 classes: 40-49, 50-59, 60-69,

70-79, 80-89, and 90-99. Express the cumulative relative frequency to two decimal places.

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

Scores Frequency Relative

Frequency

Cumulative

Relative

Frequency

40 - 49

50 - 59

60 - 69

70 - 79

80 - 89

90 - 99

(b) What percentage of the midterm exam scores was at least 80?

4. Answer the following questions based on the midterm exam score data given in Question # 3:

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

(a) What is the range of the midterm exam scores?

(b) What is the median of the midterm exam scores?

STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 4 of 10

5. A STAT 200 professor took a sample of 10 midterm exam scores from a class of 30 students. The

10 scores are shown in the table below:

95 68 76 51 85 70 89 84 67 72

(a) What is the sample mean?

(b) What is the sample standard deviation? (Round your answer to two decimal places)

did you use? If an online applet was used, please list the URL, and describe the steps. If a

calculator or Excel was used, please write out the function.

6. There are 4 suits (heart, diamond, clover, and spade) in a 52-card deck, and each suit has 13

cards. Suppose your experiment is to draw one card from a deck and observe what suit it is.

Express the probability in fraction format. (Show all work. Just the answer, without supporting

work, will receive no credit.)

(a) Find the probability of drawing a diamond or clover.

(b) Find the probability that the card is not a spade.

7. There are 6 white balls and 4 red balls in an urn. Consider selecting one ball at a time from the

urn. What is the probability that the first ball is white and the second ball is also white? Express

the probability in fraction format. (Show all work. Just the answer, without supporting work, will

receive no credit.)

(a) Assuming the ball selection is with replacement.

(b) Assuming the ball selection is without replacement.

8. There are twenty stores for a grocery chain in the Mid-Atlantic region. The regional executive

wants to visit five of the twenty stores. She asks her assistant to choose five stores and arrange the

visit schedule. (Show all work. Just the answer, without supporting work, will receive no credit).

(a) Does the order matter in the scheduling?

(b) Based on your answer to part (a), should you use permutation or combination to find the

different schedules that the assistant may arrange?

STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 5 of 10

9. Mimi has eight books from the Statistics is Fun series. She plans on bringing two of the eight

books with her in a road trip. (Show all work. Just the answer, without supporting work, will

receive no credit).

(a) Does the order matter in the book selection?

(b) Based on your answer to part (a), should you use permutation or combination to find the

number of the different ways the two books can be selected?

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

(a) Construct a table describing the probability distribution.

x P(x)

(b) Determine the mean and standard deviation of x. Show all work. Just the answer, without supporting

work, will receive no credit.

11. Mimi joined UMUC basketball team since summer 2018. On average, she is able to score 30% of the

field goals. Assume she tries 15 field goals in a game.

(a) Let X be the number of field goals that Mimi scores in the game. 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 Mimi scores at least 5 of the 15 field goals. (Round the answer to 3 decimal

places).

list the URL and describe the steps. If a calculator or Excel was used, write out the function.

12. The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation

of 2 feet. Show all work. Just the answer, without supporting work, will receive no credit.

(a) What is the probability that a randomly selected pecan tree is between 8.5 and 12.5 feet tall?

(round the answer to 4 decimal places)

(b) Find the 90th percentile of the pecan tree height distribution. (round the answer to 2 decimal places)

STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 6 of 10

used, list the URL and describe the steps. If a calculator or Excel was used, write out the function

13. Based on the performance of all individuals who tested between July 1, 2014 and June 30, 2017,

the GRE Quantitative Reasoning scores are normally distributed with a mean of 152.8 and a

standard deviation of 9.13. (https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). Show all work.

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

(a) Consider all random samples of 36 test scores. What is the standard deviation of the sample

means? (Round your answer to three decimal places)

(b) What is the probability that 36 randomly selected test scores will have a mean test score that is

between 150 and 155? (Round your answer to four decimal places)

URL and describe the steps. If a calculator or Excel was used, write out the function

14. A survey showed that 850 of the 1600 adult respondents who live in a household without landline

phones.

(a) Construct a 95% confidence interval estimate of the proportion of adults living in a household

without landline phones. Show all work. Just the answer, without supporting work, will receive no

credit. Include description of how confidence interval was constructed.

(b) Describe the confidence interval in everyday language.

15. A random sample of 900 SAT scores has a sample mean of 1100. Assume that SAT scores have a

population standard deviation of 300.

(a) Construct a 95% confidence interval estimate of the mean SAT scores. Show all work. Just the

answer, without supporting work, will receive no credit. Include description of how confidence

interval was constructed.

(b) Describe the confidence interval in everyday language.

https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf

STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 7 of 10

16. A researcher claims the proportion of adults who live in a household without landline phones is

greater than 50%. A survey showed that 850 of the 1600 adult respondents who live in a

household without landline phones.

Assume you want 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: one-sample z-test for the

population proportion, one-sample t-test for population proportion, one-sample z-test for

population mean, or one-sample t- test for population mean? Please identify and explain why it is

appropriate.

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

correct test statistic, without supporting work, will receive no credit.

(d) Determine the P-value for this test. Round your answer to three decimal places. Show all work;

writing the correct P-value, without supporting work, will receive no credit.

(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 adults living in a

household without landline phones is greater than 50%? Explain.

STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 8 of 10

17. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words.

Each was asked to list as many of the words as he or she could remember both 1 hour and 24

hours later. The result is shown in the following table.

Number of Words Recalled

Subject 1 hour later 24 hours later

1 14 12

2 18 15

3 11 9

4 13 12

5 12 12

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the

mean recall after 24 hours?

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

(a) What is the appropriate hypothesis test to use for this analysis: z-test for two proportions, t-test for

two proportions, t-test for two dependent samples (matched pairs), or t-test for two independent

samples? Please identify and explain why it is appropriate.

(b) Let μ1 = mean number of words recalled 1 hour later. Let μ2 = mean number of words recalled 24

hours later. 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)

hours later. 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. Show all work; writing the

correct test statistic, without supporting work, will receive no credit.

(e) Determine the p-value. Round your answer to three decimal places. Show all work; writing the

correct critical value, without supporting work, will receive no credit.

(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) Is there sufficient evidence to support the claim that the mean number of words recalled after 1

hour exceeds the mean recall after 24 hours? Justify your conclusion.

STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 9 of 10

18. 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 38 22 13 9 18

(a) What is the appropriate hypothesis test: z-test for sample proportion, t-test for sample mean, chi-

square goodness of fit test, F-test for ANOVA? Please identify and explain why it is appropriate

for analyzing this data.

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

correct test statistic, without supporting work, will receive no credit.

(d) Determine the P-value. Round your answer to two decimal places. Show all work; writing the

correct P-value, without supporting work, will receive no credit.

(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 published color distribution is correct?

Justify your answer.

19. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score.

A random sample of 10 students produced the following data where x is the average quiz score and

y is the final exam score.

x 86 95 50 65 98 55 85 70 75 85

y 85 96 60 63 96 60 83 60 77 87

(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. 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 final exam score if the average quiz

score is 80? Show all work and justify your answer.

score is 40? Show all work and justify your answer.

(d) Which predicted final exam score that you calculated for (b) and (c) do you think is closer to the

true final exam score and why?

STAT 200: Introduction to Statistics Final Examination, Fall 2018 OL4_US2 Page 10 of 10

20. What is the appropriate statistical analysis to use: t-test for two independent samples, t-test for two

dependent samples, ANOVA, or chi-square test of independence? Please identify and explain why

it is appropriate.

(a) 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.

(b) A study was conducted to see whether the mean weight loss is the same for 10 different weight

loss programs. Each of the 10 programs had 50 subjects in it. The subjects were followed for

12 months. Weight change for each subject was recorded.