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STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL1

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STAT 200

OL1/US1 Sections

Final Exam

Spring 2019

The final exam will be posted at 12:01 am on March 8, 2019, and

it is due at 11:59 pm on March 10, 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 OL1

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1. The World Health Organization wishes to estimate the mean density of people per square kilometer,

they collect data on 56 countries. Justify for full credit.

(a) Which of the followings is the variable?

(i) All countries in the world

(ii) Density of people per square kilometer

(iii) Set of densities of people per square kilometer of all countries

(iv) Set of densities of people per square kilometer of 56 countries

(b) Which of the followings is the population?

(i) All countries in the world

(ii) Density of people per square kilometer

(iii) Set of densities of people per square kilometer of all countries

(iv) Set of densities of people per square kilometer of 56 countries

2. In order to collect data on the cars that your classmates drive, you plan on asking them: “What brand

of car do you drive?” Justify for full credit.

(a) Which type of measurement scale is your data?

(i) Ratio

(ii) Nominal

(iii) Interval

(iv) Ordinal

(b) Which center measures can be used to summarize your data?

(i) Mean

(ii) Median

(iii) Mode

(iv) Variance

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL1

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

(a) 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) interval

(ii) nominal

(iii) ordinal

(iv) ratio

(b) A STAT 200 instructor surveyed nearly 100 students, who took STAT 200 in Fall 2018, and

asked how many hours they spent on STAT 200 each week. The average hours spent was 12.25

hours. The value 12.25 is a:

(i) parameter

(ii) statistic

(iii) population

(iv) sample

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.

5. 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 OL1

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6. 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 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?

7. A random sample of 100 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 8 2.0 – 2.9 22 3.0 – 3.9 0.84

4.0 – 5.9 0.98

6.0 – 6.9 1.00

Total 100

(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 3 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 – 5.9, or 6.0 – 6.9? Why?

8. Consider selecting one card at a time from a 52-card deck. What is the probability that the first card is an ace and the second card is also an ace? Express the probability in fraction format. (Note: There

are 4 aces 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.

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL1

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9. UMUC Stat Club must appoint a president, a vice president, and a treasurer. There are 10 qualified candidates.

(a) How many different ways can the officers be appointed?

(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. 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.

(a) How many different ways can the two books 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.

11. 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 0.22

2 0.45

3 0.18

4 0.05

(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 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 8 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 she returns at least 1 of the 8 serves from her opponent. (Round the

answer to 3 decimal places) Show all work. Just the answer, without supporting work, will

receive no credit.

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL1

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13. 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 15 and 30 miles per gallon?

(Round the answer to 4 decimal places)

(b) Find the 75th percentile of the gas mileage distribution. (Round the answer to 2 decimal places)

14. Based on the performance of all individuals who tested between 2015 and 2017, the GMAT total

scores are normally distributed with a mean of 561.27 and a standard deviation of 119.31.

(https://www.gmac.com/gmat-other-assessments/accessing-gmat-exam-scores-and-reports/gmat-

scoring-by-exam-section-normal-view#tab5). Show all work. Just the answer, without supporting

work, will receive no credit.

(a) For a sample of size 100, 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 100 is taken. Find the probability that the sample mean GMAT total

scores is more than 575. (Round your answer to three decimal places) 15. The UMUC MiniMart sells four different types of teddy bears. The manager reports that the four

types are equally popular. Suppose that a sample of 100 purchases yields observed counts 30, 24,

22, and 24 for types 1, 2, 3, and 4, respectively.

Type 1 2 3 4

Number 30 24 22 24

Use a 0.10 significance level to test the claim that the four types are equally popular.

(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 four types are equally popular? Justify your answer.

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL1

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16. A survey showed that 720 of the 1000 adult respondents believe in global warming.

(a) Construct a 90% 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.

17. In a study to assess the effectiveness of garlic for lowering cholesterol, 50 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 8 and a standard deviation of 4.

(a) Construct a 95% 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.

18. A researcher claims that more than 75% of the adults believe in global warming. Mimi conducted a survey on a random sample of 200 adults. The survey showed that 155 adults in the sample believe

in global warming. Assume Mimi 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 more than 75% of the adults believe in global warming? Explain your conclusion.

STAT 200: Introduction to Statistics Final Examination, Spring 2019 OL1

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19. A health educator was interested in determining whether college students at her college really do gain weight during their freshman year. A random sample of 5 college students was chosen and the weight

for each student was recorded in August (the beginning of the freshman year) and May (the end of

the freshman year). 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

180 182

170 175

135 140

162 160

200 200

(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, Spring 2019 OL1

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20. A scientist believes that the frequency of cricket chirping is a good predictor of the ambient

temperature. A random sample produced the following data where x is the number of cricket chirps in

one minute and y is the ambient temperature in Fahrenheit.

x y

128 70

227 93

188 84

150 76

210 89

185 83

137 72

171 80

(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 temperature when a cricket chirps 300 times in one minute? Show all work and justify your answer.

(c) Based on the equation from part (a), what is the predicted temperature when a cricket chirps 140 times in one minute? Show all work and justify your answer.

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