# STAT200 : Introduction to Statistics Final Examination, Fall 2014

1. Determine whether the given value is a statistic or parameter. (4 pts)

(a) In a STAT 200 student survey, 20% of the respondents said that they had to take time off from work to study for the course.

(b) The average lifetime of all street lights in UMUC Academic Center is 20,000 hours.

2. True of False. (8 pts)

(a) Mean is a better measure of center than median because mean is not affected by extreme values from a data set.

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

(c) It is possible that a data set does not have a mode.

(d) P(AandA) 1, whereAis the complement ofA.

Refer to the following frequency distribution for Questions 3, 4, 5, and 6. Show all work. Just the answer, without supporting work, will receive no credit.

The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes) Frequency

1.0 - 1.9 6

2.0 - 2.9 5

3.0 - 3.9 4

4.0 - 4.9 3

5.0 - 5.9 2

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 3 of 6

3. What percentage of the checkout times was at least 4 minutes? (5 pts)

4. Calculate the mean of this frequency distribution. (5 pts)

5. Calculate the standard deviation of this frequency distribution. (Round the answer to two

decimal places) (10 pts)

6. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were incorrectly recorded as 0.12 instead of 1.2. Will the mean increase,

decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers. (5 pts)

Refer to the following data to answer questions 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of STAT200 weekly study times in hours is as follows:

1 13 15 18 20

7. Find the standard deviation. (Round the answer to two decimal places) (10 pts)

8. Are any of these study times considered unusual based on the Range Rule of Thumb?

Show work and explain. (5 pts)

Refer to the following information for Questions 9, 10 and 11. Show all work. Just the answer, without supporting work, will receive no credit.

Consider selecting one card at a time without replacement from a 52-card deck. Let event A be the first card is a heart, and event B be the second card is a heart.

9. What is the probability that the first card is a heart and the second card is also a heart?

(Express the answer in simplest fraction form) (8 pts)

10. What is the probability that the second card is a heart, given that the first card is a heart?

(Express the answer in simplest fraction form) (8 pts)

11. Are A and B independent? Why or why not? (2 pts)

Refer to the following information for Questions 12 and 13. Show all work. Just the answer, without supporting work, will receive no credit.

There are 1500 juniors in a college. Among the 1500 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.

12. What is the probability that a randomly selected junior is in neither of the two courses?

(10 pts) 13. What is the probability that a randomly selected junior takes only one course? (10 pts)

Refer to the following information for Questions 14, and 15. Show all work. Just the answer, without supporting work, will receive no credit.

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 4 of 6

UMUC STAT Club must appoint a president, a vice president, and a treasurer. It must also select three members for the STAT Olympics team. There are 10 qualified candidates, and officers can also be on the STAT Olympics team.

14. How many different ways can the officers be appointed? (10 pts)

15. How many different ways can the STAT Olympics team be selected? (10 pts)

Questions 16 and 17 involve the random variable x with probability distribution given below.

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

x -1 0 1 2 5

P(x) 0.1 0.1 0.4 0.1 0.3

16. Determine the expected value of x. (5 pts)

17. Determine the standard deviation of x.(Round the answer to two decimal places) (10 pts)

Consider the following situation for Questions 18, 19 and 20. Show all work. Just the answer, without supporting work, will receive no credit.

Mimi made random guesses at 5 true-or-false questions in a STAT 200 pop quiz. Let random number X be the number of correct answers Mimi got. As we know, the distribution of X is a binomial probability distribution. Please answer the following questions:

18. What is the number of trials (n), probability of successes (p) and probability of failures (q),

respectively? (5 pts)

19. Find the probability that she got at least 3 correct answers . (10 pts)

20. Find the mean and standard deviation for the probability distribution. (Round the answer to two

decimal places) (10 pts)

Refer to the following information for Questions 21, 22, and 23. Show all work. Just the answer, without supporting work, will receive no credit.

The heights of dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.

21. What is the probability that a randomly selected dogwood tree is between 6 and 15 feet tall?

(10 pts)

22. Find the 80th percentile of the dogwood tree height distribution. (5 pts)

23. If a random sample of 144 dogwood trees is selected, what is the standard deviation of the sample

mean? (5 pts)

24. A random sample of 100 GMAT scores has a mean of 500. Assume that GMAT scoreshave a population standard deviation of 120. Construct a 95% confidence interval estimate of the

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 5 of 6

mean GMAT scores. Show all work. Just the answer, without supporting work, will receive no credit.

(15 pts)

25. Given a sample size of 100, with sample mean 730 and sample standard deviation 100,

we perform the following hypothesis test at the 0.05 level.

H0: 750

H1: 750

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the critical value. Show all work; writing the correct critical value,

without supporting work, will receive no credit.

(c) What is your conclusion of the test? Please explain. (20 pts)

26. Consider the hypothesis test given by

H 0: p 0.5 H1: p 0.5

In a random sample of 225 subjects, the sample proportion is found to be pˆ 0.55 .

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of H0 at the0.01 level?

Explain. (20 pts)

27. 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 10

2 18 14

3 11 9

4 16 12

5 15 12

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 6 of 6

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3?

Assume we want to use a 0.01 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 critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) 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 by more than 3? Justify your conclusion. (25 pts)

Refer to the following data for Questions 28 and 29.

x 0 -1 3 2 5

y 3 -2 3 6 8

28. Find an equation of the least squares regression line. Show all work; writing the correct

equation, without supporting work, will receive no credit. (15 pts)

29. Based on the equation from # 28, what is the predicted value of y if x = 4? Show all work

and justify your answer. (10 pts)

30. The UMUC Bookstore sells three different types of coffee mugs. The manager reported

that the three types are purchased in proportions: 50%, 30%, and 20%, respectively.

Suppose that a sample of 100 purchases yields observed counts 46, 28, and 26 for types

1, 2, and 3, respectively.

Type 1 2 3

Number 46 28 26

Assume we want to use a 0.10 significance level to test the claim that the reported

proportions are correct.

(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 critical value. Show all work; writing the correct critical value,

without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that the reported proportions are

correct? Justify your answer. (25 pts)

(a) In a STAT 200 student survey, 20% of the respondents said that they had to take time off from work to study for the course.

(b) The average lifetime of all street lights in UMUC Academic Center is 20,000 hours.

2. True of False. (8 pts)

(a) Mean is a better measure of center than median because mean is not affected by extreme values from a data set.

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

(c) It is possible that a data set does not have a mode.

(d) P(AandA) 1, whereAis the complement ofA.

Refer to the following frequency distribution for Questions 3, 4, 5, and 6. Show all work. Just the answer, without supporting work, will receive no credit.

The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes) Frequency

1.0 - 1.9 6

2.0 - 2.9 5

3.0 - 3.9 4

4.0 - 4.9 3

5.0 - 5.9 2

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 3 of 6

3. What percentage of the checkout times was at least 4 minutes? (5 pts)

4. Calculate the mean of this frequency distribution. (5 pts)

5. Calculate the standard deviation of this frequency distribution. (Round the answer to two

decimal places) (10 pts)

6. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were incorrectly recorded as 0.12 instead of 1.2. Will the mean increase,

decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers. (5 pts)

Refer to the following data to answer questions 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of STAT200 weekly study times in hours is as follows:

1 13 15 18 20

7. Find the standard deviation. (Round the answer to two decimal places) (10 pts)

8. Are any of these study times considered unusual based on the Range Rule of Thumb?

Show work and explain. (5 pts)

Refer to the following information for Questions 9, 10 and 11. Show all work. Just the answer, without supporting work, will receive no credit.

Consider selecting one card at a time without replacement from a 52-card deck. Let event A be the first card is a heart, and event B be the second card is a heart.

9. What is the probability that the first card is a heart and the second card is also a heart?

(Express the answer in simplest fraction form) (8 pts)

10. What is the probability that the second card is a heart, given that the first card is a heart?

(Express the answer in simplest fraction form) (8 pts)

11. Are A and B independent? Why or why not? (2 pts)

Refer to the following information for Questions 12 and 13. Show all work. Just the answer, without supporting work, will receive no credit.

There are 1500 juniors in a college. Among the 1500 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.

12. What is the probability that a randomly selected junior is in neither of the two courses?

(10 pts) 13. What is the probability that a randomly selected junior takes only one course? (10 pts)

Refer to the following information for Questions 14, and 15. Show all work. Just the answer, without supporting work, will receive no credit.

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 4 of 6

UMUC STAT Club must appoint a president, a vice president, and a treasurer. It must also select three members for the STAT Olympics team. There are 10 qualified candidates, and officers can also be on the STAT Olympics team.

14. How many different ways can the officers be appointed? (10 pts)

15. How many different ways can the STAT Olympics team be selected? (10 pts)

Questions 16 and 17 involve the random variable x with probability distribution given below.

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

x -1 0 1 2 5

P(x) 0.1 0.1 0.4 0.1 0.3

16. Determine the expected value of x. (5 pts)

17. Determine the standard deviation of x.(Round the answer to two decimal places) (10 pts)

Consider the following situation for Questions 18, 19 and 20. Show all work. Just the answer, without supporting work, will receive no credit.

Mimi made random guesses at 5 true-or-false questions in a STAT 200 pop quiz. Let random number X be the number of correct answers Mimi got. As we know, the distribution of X is a binomial probability distribution. Please answer the following questions:

18. What is the number of trials (n), probability of successes (p) and probability of failures (q),

respectively? (5 pts)

19. Find the probability that she got at least 3 correct answers . (10 pts)

20. Find the mean and standard deviation for the probability distribution. (Round the answer to two

decimal places) (10 pts)

Refer to the following information for Questions 21, 22, and 23. Show all work. Just the answer, without supporting work, will receive no credit.

The heights of dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.

21. What is the probability that a randomly selected dogwood tree is between 6 and 15 feet tall?

(10 pts)

22. Find the 80th percentile of the dogwood tree height distribution. (5 pts)

23. If a random sample of 144 dogwood trees is selected, what is the standard deviation of the sample

mean? (5 pts)

24. A random sample of 100 GMAT scores has a mean of 500. Assume that GMAT scoreshave a population standard deviation of 120. Construct a 95% confidence interval estimate of the

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 5 of 6

mean GMAT scores. Show all work. Just the answer, without supporting work, will receive no credit.

(15 pts)

25. Given a sample size of 100, with sample mean 730 and sample standard deviation 100,

we perform the following hypothesis test at the 0.05 level.

H0: 750

H1: 750

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the critical value. Show all work; writing the correct critical value,

without supporting work, will receive no credit.

(c) What is your conclusion of the test? Please explain. (20 pts)

26. Consider the hypothesis test given by

H 0: p 0.5 H1: p 0.5

In a random sample of 225 subjects, the sample proportion is found to be pˆ 0.55 .

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of H0 at the0.01 level?

Explain. (20 pts)

27. 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 10

2 18 14

3 11 9

4 16 12

5 15 12

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 6 of 6

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3?

Assume we want to use a 0.01 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 critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) 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 by more than 3? Justify your conclusion. (25 pts)

Refer to the following data for Questions 28 and 29.

x 0 -1 3 2 5

y 3 -2 3 6 8

28. Find an equation of the least squares regression line. Show all work; writing the correct

equation, without supporting work, will receive no credit. (15 pts)

29. Based on the equation from # 28, what is the predicted value of y if x = 4? Show all work

and justify your answer. (10 pts)

30. The UMUC Bookstore sells three different types of coffee mugs. The manager reported

that the three types are purchased in proportions: 50%, 30%, and 20%, respectively.

Suppose that a sample of 100 purchases yields observed counts 46, 28, and 26 for types

1, 2, and 3, respectively.

Type 1 2 3

Number 46 28 26

Assume we want to use a 0.10 significance level to test the claim that the reported

proportions are correct.

(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 critical value. Show all work; writing the correct critical value,

without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that the reported proportions are

correct? Justify your answer. (25 pts)

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