STATISTICS 200

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL3

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STAT 200

OL3 Sections

Final Exam

Spring 2019

The final exam will be posted at 12:01 am on April 19, 2019, and

it is due at 11:59 pm on April 21, 2019 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, Spring 2019 OL3

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1. You wish to estimate the mean cholesterol levels of patients two days after they had a heart attack. To

estimate the mean, you collect data from 28 heart patients. Justify for full credit.

(a) Which of the followings is the sample?

(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two

days ago

(ii) Cholesterol level of the person recovering from heart attack suffered two days ago

(iii) Set of all patients recovering from a heart attack suffered two days ago

(iv) Set of 28 patients recovering from a heart attack suffered two days ago

(b) Which of the followings is the variable?

(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two

days ago

(ii) Cholesterol level of the person recovering from heart attack suffered two days ago

(iii) Set of all patients recovering from a heart attack suffered two days ago

(iv) Set of 28 patients recovering from a heart attack suffered two days ago

2. In order to collect data on the number of courses that your classmates take in this semester, you plan

on asking them: “How many UMUC courses are you taking in this semester? “Justify for full credit.

(a) Which type of data will you collect?

(i) Discrete

(ii) Continuous

(iii) Qualitative

(iv) Cannot be determined

(b) Which measure of variation can be used to summarize your data?

(i) Mean

(ii) Median

(iii) Mode

(iv) Variance

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL3

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3. True or False. Justify for full credit.

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

must be identical.

(b) The median of a normal distribution curve is always zero.

4. A STAT 200 student is interested in the number of credit cards owned by college students. She

surveyed all of her classmates to collect sample data.

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

5. A study was conducted to determine whether the mean braking distance of four-cylinder cars is

greater than the mean braking distance of six-cylinder cars. A random sample of 20 four-cylinder cars

and a random sample of 20 six-cylinder cars were obtained, and the braking distances were measured.

(a) What would be the appropriate hypothesis test for this analysis?

(i) t-test for two dependent samples

(ii) t-test for two independent samples

(iii) z-test for two population means

(iv) correlation

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

statistical approach?

6. A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50

subjects in it. The subjects were followed for 12 months. Weight change for each subject was

recorded. The researcher wants to test the claim that all ten programs are equally effective in weight

loss.

(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?

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL3

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7. A random sample of 80 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in

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

Checkout Time (in

Minutes) Frequency

Cumulative Relative

Frequency

1.0 – 1.9 0.10

2.0 – 2.9 0.65

3.0 – 3.9 16

4.0 – 4.9 8

5.0 – 5.9 4 1.00

Total 80

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

(b) What percentage of the checkout times was less than 4 minutes? (c) Which of the following checkout time groups does the median of this distribution belong

to? 1.0 – 1.9, 2.0 – 2.9, 3.0 – 3.9, 4.0 – 4.9, or 5.0 – 5.9? Why?

8. There are 15 members on the board of directors for a Fortune 500 company. If they must select a

chairperson, a first vice chairperson, a second vice chairperson, and a secretary.

(a) How many different ways the officers can 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.

9. A researcher wants to conduct a clinical trial on a new medicine for a rare disease. She plans to randomly choose 4 testers from 20 eligible patients.

(a) How many different ways can the testers be chosen?

(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.

10. Consider selecting one ball at a time from a box which contains 10 red, 6 yellow and 4 blue balls. What is the probability that the first ball is yellow and the second ball is also yellow? 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 without replacement.

(b) Assuming the ball selection is with replacement.

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL3

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11. An airline company has a policy of routinely overbooking flights. The following probability distribution table shows the random variable, x, where x is number of passengers who cannot be

boarded because there are more passengers than seats:

x P(x)

0 0.07

1 0.14

2 0.27

3 0.33

4 0.19

(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.

12. Mimi plans on growing tomatoes in her garden. She has 15 cherry tomato seeds. Based on her

experience, the probability of a seed turning into a seedling is 0.60.

(a) Let X be the number of seedlings 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 she gets at least 10 cherry tomato seedlings. (Round the answer to 3

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

credit.

Refer to the following information for Questions 13 and 14.

The heights of pecan trees are normally distributed with a mean of 10 feet and a

standard deviation of 2 feet.

13. 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 9 and 12 feet tall?

(Round the answer to 4 decimal places)

(b) Find the 80th percentile of the pecan tree height distribution. (Round the answer to 2 decimal places)

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

(a) For a sample of 36 pecan trees, 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 36 pecan trees is taken. Find the probability that the sample mean

heights is between 9.5 and 10 feet. (Round your answer to four decimal places)

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL3

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15. A survey showed that 750 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.

16. A bike company wants to determine how long children have to use training wheels when learning to

ride two-wheel bikes. The company surveyed a random sample of 64 children. The result showed that

they used an average of 180 days with a sample standard deviation of 100 days.

(a) Construct a 95% confidence interval estimate of the mean length of time using training wheels.

(Round the lower bound and upper bound of the confidence interval to whole number) Include

description of how confidence interval was constructed.

(b) Describe the confidence interval in everyday language.

17. An AP Statistics teacher claims that the AP Statistics grade distribution is as follows:

Grade A B C D F

Percentage 20% 40% 20% 15% 5%

Suppose that a sample of 100 students taking AP Statistics class yields the observed counts shown

below:

Grade A B C D F

Number of

Students 25 35 15 17 8

Use a 0.10 significance level to test the claimed AP Statistics grade distribution is correct.

(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 that the claimed AP Statistics grade distribution is correct? Justify your answer.

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL3

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18. 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.

Does the data below 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.

Number of Words Recalled

Subject 1 hour later 24 hours later

1 14 12

2 18 14

3 11 8

4 13 12

5 12 12

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

it is appropriate.

(b) Let μ1 = mean words recalled after 1 hour. Let μ2 = mean words recalled after 24 hours. 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 words recalled after 1 hour. Let μ2 = mean words recalled after 24 hours. 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 the mean number of words recalled after 1 hours and after 24 hours? Justify your conclusion.

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL3

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19. A grocery store manager is interested in testing the claim that banana is the favorite fruit for more than 50% of the adults. The manager conducted a survey on a random sample of 100 adults. The

survey showed that 56 adults in the sample chose banana as his/her favorite fruit. Assume the

manager wants to use a 0.05 significance level to test the 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 claim that banana is the favorite fruit for more than 50% of the adults? Explain your conclusion.

20. A random sample of 8 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 y

0 1

1 1.5

1 2

2 3

2 3.5

3 3

5 6.5

5 7

(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 amount of money made when a professional athlete has 4 endorsements? Show all work and justify your answer.

(c) Based on the equation from part (a), what is the predicted amount of money made when a professional athlete has 15 endorsements? Show all work and justify your answer.

(d) Which predicted amount of money made that you calculated for (b) and (c) do you think is closer to the true amount of the money made and why?