STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 1 of 8STAT 200OL2 SectionsFinal ExamSummer 2016The final exam will be posted at 12: 01 am on July 22, and it is dueat 11: 59 pm on July 24, 2016. Eastern Time is our reference time. This is an open-book exam. You may refer to your text and other course materialsas you work on the exam, and you may use a calculator. You must complete theexam individually. Neither collaboration nor consultation with others is allowed. It is a violation of the UMUC Academic Dishonesty and Plagiarism policy to useunauthorized 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 straightfrom calculators, programs or software packages without any explanation will notbe accepted. If you need to use technology (for example, Excel, online or handheldcalculators, statistical packages) to aid in your calculation, you must cite thesources and explain how you get the results. Record your answers and work on the separate answer sheet provided. This exam has 200 total points, 10 points 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, Summer 2016 OL2 Page 2 of 81. True or False. Justify for full credit. (a) If P(A) = 0. 4, P(B) = 0. 5, and A and B are independent, then P(A AND B) = 0. 2. (b) If the variance of a data set is 0, then all the observations in this data set must be zero. (c) The mean is always equal to the median for a normal distribution. (d) A 90% confidence interval is wider than a 95% confidence interval of the same parameter. (e) In a right-tailed test, the value of the test statistic is 2. The test statistic follows a distributionwith the distribution curve shown below. If we know the shaded area is 0. 96, then we havesufficient evidence to reject the null hypothesis at 0. 05 level of significance. 2. Choose the best answer. Justify for full credit. (a) UMUC Stat Club conducted a survey on STAT 200 study hours. The survey result showedthat 54% of the respondents spent more than 20 hours each week on STAT 200. The value54% is a(i) statistic(ii) parameter(iii) cannot be determined(b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is(i) interval(ii) nominal(iii) ordinal(iv) ratio(c) UMUC STAT Club wanted to estimate the study hours of STAT 200 students. Two STAT 200sections were randomly selected and all students from these two sections were asked to fill outthe questionnaire. This type of sampling is called: (i) cluster(ii) convenience(iii) systematic(iv) stratifiedSTAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 3 of 83. Choose the best answer. Justify for full credit. (a) A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programshad 50 subjects in it. The subjects were followed for 12 months. Weight change for eachsubject was recorded. You want to test the claim that the mean weight loss is the same for the10 programs. What statistical approach should be used?(i) t-test(ii) linear regression(iii) ANOVA(iv) confidence interval(b) A STAT 200 instructor teaches two classes. She wants to test if the variances of the scoredistribution for the two classes are different. What type of hypothesis test should she use?(i) t-test for two independent samples(ii) t-test for matched samples(iii) z-test for two samples(iv) F- test4. The frequency distribution below shows the distribution for IQ scores for a random sample of1000 adults. (Show all work. Just the answer, without supporting work, will receive no credit. )IQ Scores Frequency Relative Frequency50 – 69 2470 – 89 22890 -109 493110 – 129 0. 23130 – 149 25Total 1000(a) Complete the frequency table with frequency and relative frequency. Express the relativefrequency to three decimal places. (b) What percentage of the adults in this sample has an IQ score of at least 110?(c) Does this distribution have positive skew or negative skew? Why or why not? STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 4 of 85. The boxplots below show the grade distribution of two STAT 200 quizzes for a sample of 500students. For each question, give your answer as one of the following: (i) Quiz 1, (ii) Quiz 2, (iii) Both quizzeshave the same value requested, (iv) It is impossible to tell using only the given information. Thenexplain your answer in each case. (a) Which quiz has greater range in grade distribution?(b) Which quiz has the lower percentage of students with grades 85 and over?(c) Which quiz has a greater percentage of students with grades less than 60?6. A sample of 10 LED light bulbs consists of 1 defective and 9 good light bulbs. A qualitycontrol technician wants to randomly select two of the light bulbs for inspection. Find theprobability that the first selected light bulb is good and the second light bulb is also good. (Show all work. Just the answer, without supporting work, will receive no credit. )(a) Assuming the two random selections are made with replacement. (b) Assuming the two random selections are made without replacement. 7. There are 1000 students in a high school. Among the 1000 students, 200 students take APStatistics, and 250 students take AP French. 100 students take both AP courses. Let S be theevent that a randomly selected student takes AP Statistics, and F be the event that a randomlyselected student takes AP French. Show all work. Just the answer, without supporting work,will receive no credit. (a) Provide a written description of the event (S OR F). (b) What is the probability of complement event of (S OR F)?STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 5 of 88. Consider rolling two fair dice. Let A be the event that the sum of the two dice is 7, and B bethe event that the first one is an even number. (a) What is the probability that the sum of the two dice is 7 given that the first one is an evennumber? Show all work. Just the answer, without supporting work, will receive no credit. (b) Are event A and event B independent? Explain. 9. Answer the following two questions. (Show all work. Just the answer, without supportingwork, will receive no credit). (a) There are 15 juniors and 20 seniors in the UMUC Stat Club. The club is to send fourrepresentatives to the Joint Statistical Meetings. If the members of the club decide to send twojuniors and two seniors, how many different groupings are possible?(b) A bike courier needs to make deliveries at 6 different locations. How many different routes canhe take?10. Assume random variable x follows a probability distribution shown in the table below. Determine the mean and standard deviation of x. Show all work. Just the answer, withoutsupporting work, will receive no credit. x -2 0 1 2 3P(x) 0. 1 0. 1 0. 3 0. 2 0. 311. Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 cucumbers in her gardenwhich will be ready to harvest in about 10 days. Based on her experience, the probability of acucumber being eaten by the rabbits before harvest is 0. 30. (a) Let X be the number of cucumbers that Mimi harvests (that is, the number of cucumbers noteaten by rabbits). 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 harvests at most 8 of the 10 cucumbers. (round the answer to 3decimal places) Show all work. Just the answer, without supporting work, will receive no credit. 12. Assume the weights of men are normally distributed with a mean of 170 lbs and a standarddeviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive nocredit. (a) Find the 75th percentile for the distribution of men’s weights. (b) What is the probability that a randomly selected man weighs more than 200 lbs?STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 6 of 813. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500and a standard deviation of 100. Show all work. Just the answer, without supporting work, willreceive no credit. (a) If a random sample of 64 test scores is selected, what is the standard deviation of the samplemean?(b) What is the probability that 64 randomly selected test scores will have a mean test score that isbetween 475 and 525?14. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a90% confidence interval estimate of the proportion of adults believing in global warming. Showall work. Just the answer, without supporting work, will receive no credit. 15. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults weretreated with garlic tablets. Cholesterol levels were measured before and after the treatment. Thechanges in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14. Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after thegarlic tablet treatment. Show all work. Just the answer, without supporting work, will receiveno credit. 16. Mimi is interested in testing the claim that banana is the favorite fruit for more than 50% of theadults. She conducted a survey on a random sample of 100 adults. 58 adults in the samplechose banana as his / her favorite fruit. Assume Mimi wants to use a 0. 10 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 supportingwork, will receive no credit. (c) Determine the P-value for this test. Show all work, writing the correct P-value, withoutsupporting work, will receive no credit. (d) Is there sufficient evidence to support the claim that banana is the favorite fruit for more than50% of the adults? Explain. 17. In a study of freshman weight gain, the measured weights of 5 randomly selected collegestudents in September and April of their freshman year are shown in the following table. Weight (kg)Student September April1 67 662 53 553 64 684 71 705 70 75Is there evidence to suggest that the mean weight of the freshmen in April is greater than themean weight in September? STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 7 of 8Assume we want to use a 0. 10 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 supportingwork, will receive no credit. (c) Determine the P-value for this test. Show all work, writing the correct P-value, withoutsupporting work, will receive no credit. (d) Is there sufficient evidence to support the claim that the mean weight of the freshmen in Aprilis greater than the mean weight in September? Justify your conclusion. 18. In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats perminute, and a standard deviation of 11. 3 beats per minute. Based on the sample results, theresearcher concludes that the pulse rates of men have a standard deviation greater than 10 beatsper minutes. Use a 0. 05 significance level to test the researcher’s claim. (a) Identify the null hypothesis and alternative hypothesis. (b) Determine the test statistic. Show all work, writing the correct test statistic, withoutsupporting work, will receive no credit. (c) Determine the P-value for this test. Show all work, writing the correct P-value, withoutsupporting work, will receive no credit. (d) Is there sufficient evidence to support the researcher’s claim? Explain. 19. The UMUC Daily News reported that the color distribution for plain M&M’s was: 40%brown, 20% yellow, 10% orange, 10% green, and 20% tan. Each piece of candy in a randomsample 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 TanNumber 42 21 12 7 18(a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work, writing the correct test statistic, withoutsupporting work, will receive no credit. (c) Determine the P-value. Show all work, writing the correct P-value, without supportingwork, will receive no credit. (d) Is there sufficient evidence to support the claim that the published color distribution iscorrect? Justify your answer. STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 8 of 820. A STAT 200 instructor believes that the average quiz score is a good predictor of final examscore. A random sample of 5 students produced the following data where x is the average quizscore and y is the final exam score. x 80 50 60 100 70y 145 150 130 180 120(a) Find an equation of the least squares regression line. Show all work, writing the correctequation, 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 quizscore is 90? Show all work and justify your answer.

Question

STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 1 of 8

STAT 200

OL2 Sections

Final Exam

Summer 2016

The final exam will be posted at 12:01 am on July 22, and it is due

at 11:59 pm on July 24, 2016. Eastern Time is our reference time.

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. 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 handheld

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 200 total points; 10 points 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, Summer 2016 OL2 Page 2 of 8

1. True or False. Justify for full credit.

(a) If P(A) = 0.4, P(B) = 0.5, and A and B are independent, then P(A AND B) = 0.2.

(b) If the variance of a data set is 0, then all the observations in this data set must be zero.

(c) The mean is always equal to the median for a normal distribution.

(d) A 90% confidence interval is wider than a 95% confidence interval of the same parameter.

(e) In a right-tailed test, the value of the test statistic is 2. The test statistic follows a distribution

with the distribution curve shown below. If we know the shaded area is 0.96, then we have

sufficient evidence to reject the null hypothesis at 0.05 level of significance.

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

(a) UMUC Stat Club conducted a survey on STAT 200 study hours. The survey result showed

that 54% of the respondents spent more than 20 hours each week on STAT 200. The value

54% is a

(i) statistic

(ii) parameter

(iii) cannot be determined

(b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is

(i) interval

(ii) nominal

(iii) ordinal

(iv) ratio

(c) UMUC STAT Club wanted to estimate the study hours of STAT 200 students. Two STAT 200

sections were randomly selected and all students from these two sections were asked to fill out

the questionnaire. This type of sampling is called:

(i) cluster

(ii) convenience

(iii) systematic

(iv) stratified

STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 3 of 8

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

(a) 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. You want to test the claim that the mean weight loss is the same for the

10 programs. What statistical approach should be used?

(i) t-test

(ii) linear regression

(iii) ANOVA

(iv) confidence interval

(b) A STAT 200 instructor teaches two classes. She wants to test if the variances of the score

distribution for the two classes are different. What type of hypothesis test should she use?

(i) t-test for two independent samples

(ii) t-test for matched samples

(iii) z-test for two samples

(iv) F- test

4. The frequency distribution below shows the distribution for IQ scores for a random sample of

1000 adults. (Show all work. Just the answer, without supporting work, will receive no credit.)

IQ Scores Frequency Relative Frequency

50 – 69 24

70 – 89 228

90 -109 493

110 – 129 0.23

130 – 149 25

Total 1000

(a) Complete the frequency table with frequency and relative frequency. Express the relative

frequency to three decimal places.

(b) What percentage of the adults in this sample has an IQ score of at least 110?

(c) Does this distribution have positive skew or negative skew? Why or why not?

STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 4 of 8

5. The boxplots below show the grade distribution of two STAT 200 quizzes for a sample of 500

students.

For each question, give your answer as one of the following: (i) Quiz 1; (ii) Quiz 2; (iii) Both quizzes

have the same value requested; (iv) It is impossible to tell using only the given information. Then

explain your answer in each case.

(a) Which quiz has greater range in grade distribution?

(b) Which quiz has the lower percentage of students with grades 85 and over?

(c) Which quiz has a greater percentage of students with grades less than 60?

6. A sample of 10 LED light bulbs consists of 1 defective and 9 good light bulbs. A quality

control technician wants to randomly select two of the light bulbs for inspection. Find the

probability that the first selected light bulb is good and the second light bulb is also good.

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

(a) Assuming the two random selections are made with replacement.

(b) Assuming the two random selections are made without replacement.

7. There are 1000 students in a high school. Among the 1000 students, 200 students take AP

Statistics, and 250 students take AP French. 100 students take both AP courses. Let S be the

event that a randomly selected student takes AP Statistics, and F be the event that a randomly

selected student takes AP French. Show all work. Just the answer, without supporting work,

will receive no credit.

(a) Provide a written description of the event (S OR F).

(b) What is the probability of complement event of (S OR F)?

STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 5 of 8

8. Consider rolling two fair dice. Let A be the event that the sum of the two dice is 7, and B be

the event that the first one is an even number.

(a) What is the probability that the sum of the two dice is 7 given that the first one is an even

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

(b) Are event A and event B independent? Explain.

9. Answer the following two questions. (Show all work. Just the answer, without supporting

work, will receive no credit).

(a) There are 15 juniors and 20 seniors in the UMUC Stat Club. The club is to send four

representatives to the Joint Statistical Meetings. If the members of the club decide to send two

juniors and two seniors, how many different groupings are possible?

(b) A bike courier needs to make deliveries at 6 different locations. How many different routes can

he take?

10. Assume random variable x follows a probability distribution shown in the table below.

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

supporting work, will receive no credit.

x -2 0 1 2 3

P(x) 0.1 0.1 0.3 0.2 0.3

11. Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 cucumbers in her garden

which will be ready to harvest in about 10 days. Based on her experience, the probability of a

cucumber being eaten by the rabbits before harvest is 0.30.

(a) Let X be the number of cucumbers that Mimi harvests (that is, the number of cucumbers not

eaten by rabbits). 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 harvests at most 8 of the 10 cucumbers. (round the answer to 3

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

12. Assume the weights of men are normally distributed with a mean of 170 lbs and a standard

deviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive no

credit.

(a) Find the 75th percentile for the distribution of men’s weights.

(b) What is the probability that a randomly selected man weighs more than 200 lbs?

STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 6 of 8

13. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500

and a standard deviation of 100. Show all work. Just the answer, without supporting work, will

receive no credit.

(a) If a random sample of 64 test scores is selected, what is the standard deviation of the sample

mean?

(b) What is the probability that 64 randomly selected test scores will have a mean test score that is

between 475 and 525?

14. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a

90% confidence interval estimate of the proportion of adults believing in global warming. Show

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

15. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were

treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The

changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14.

Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the

garlic tablet treatment. Show all work. Just the answer, without supporting work, will receive

no credit.

16. Mimi is interested in testing the claim that banana is the favorite fruit for more than 50% of the

adults. She conducted a survey on a random sample of 100 adults. 58 adults in the sample

chose banana as his / her favorite fruit.

Assume Mimi wants to use a 0.10 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 for this test. 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 banana is the favorite fruit for more than

50% of the adults? Explain.

17. In a study of freshman weight gain, the measured weights of 5 randomly selected college

students in September and April of their freshman year are shown in the following table.

Weight (kg)

Student September April

1 67 66

2 53 55

3 64 68

4 71 70

5 70 75

Is there evidence to suggest that the mean weight of the freshmen in April is greater than the

mean weight in September?

STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 7 of 8

Assume we want to use a 0.10 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 for this test. 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 the mean weight of the freshmen in April

is greater than the mean weight in September? Justify your conclusion.

18. In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats per

minute, and a standard deviation of 11.3 beats per minute. Based on the sample results, the

researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats

per minutes. Use a 0.05 significance level to test the researcher’s claim.

(a) Identify the null hypothesis and 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 this test. Show all work; writing the correct P-value, without

supporting work, will receive no credit.

(d) Is there sufficient evidence to support the researcher’s claim? Explain.

19. The UMUC Daily News reported that the color distribution for plain M&M’s was: 40%

brown, 20% yellow, 10% orange, 10% green, and 20% 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 42 21 12 7 18

(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 the published color distribution is

correct? Justify your answer.

STAT 200: Introduction to Statistics Final Examination, Summer 2016 OL2 Page 8 of 8

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

score. A random sample of 5 students produced the following data where x is the average quiz

score and y is the final exam score.

x 80 50 60 100 70

y 145 150 130 180 120

(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 final exam score if the average quiz

score is 90? Show all work and justify your answer.