Johns Hopkins University Statistics Problem Set.

### Question Description

The questions are in the pdf file.

1. A sample of 10 employees in the graphics department of Design, Inc. is selected. The

employees’ ages are given as follows:

34 35 39 24 62 40 18 35 28 35

Compute the interquartile range of ages.

a. 1

b. 11

c. 42

d. 44

e. None of these responses

2. The average grades of a sample of 8 statistics students and the number of absences they had

during the semester are given as follows:

Student # Absences Average Grade

1 1 94

2 2 78

3 2 70

4 1 88

5 3 68

6 4 40

7 8 30

8 3 60

Compute the sample covariance.

a. -0.915

b. 2.268

c. 22.168

d. -46

e. None of these responses

Answer questions 3 and 4 based on the following.

A survey of business students who had taken the Graduate Management Admissions Test

(GMAT) indicated that students who have spent at least five hours studying GMAT review

guides have a probability of 0.85 of scoring above 400. Students who do not review in this way

have a probability of 0.65 of scoring above 400. It has been determined that 70% of the business

students review for the test.

3. Compute the probability of scoring above 400.

a. 0.12

b. 0.20

c. 0.55

d. 0.79

e. 1.50

4. Given that a student scored above 400, what is the probability that he/she reviewed for the

test?

a. 0.15

b. 0.27

c. 0.60

d. 0.75

e. 0.85

5. The student body of a large university consists of 60% female students. A random sample of 8

students is selected. What is the probability that among the students in the sample at least 6

are male?

a. 0.0413

b. 0.0079

c. 0.0007

d. 0.0499

6. In a large class, suppose that your instructor tells you that you need to obtain a grade in the top

10% of your class to get an A on Exam X. From past experience, your instructor is able to

say that the mean and standard deviation on Exam X will be 72 and 13, respectively, and that

grades are distributed normally. What will be the minimum grade needed to obtain an A?

a. 88.64

b. 55.36

c. 73.28

d. 75.32

7. The travel time for a businesswoman traveling between Dallas and Fort Worth is uniformly

distributed between 40 and 90 minutes. The probability that her trip will take exactly 50

minutes is

a. 1.00

b. 0.02

c. 0.06

d. 0.20

e. 0.00

8. Consider the below population of percent tips. Would the sampling distribution of x̅ for n =

35 consist of the data point 17.09%, gotten by adding up the first seven columns of percent

tips and dividing by 35?

15 20 16 16 16 15 20 18 10 20

17 18 19 20 20 15 20 19 20 15

17 15 20 19 17 20 17 20 18 15

10 17 20 20 18 15 15 19 15 16

11 20 15 18 20 17 10 20 15 20

a. Yes

b. No

9. Refer to Question 8. Can we say that the sampling distribution of x̅ for n = 35 is distributed

normally?

a. Yes

b. No

10. Refer to Question 8. Compute the expected value of x̅ (E(x̅)) associated with the sampling

distribution of x̅ for n = 35.

a. 16.40%

b. 17.09%

c. 17.16%

d. 20.00%

e. It is not possible to compute E(x̅)

11. A local health care facility noted that in a sample of 200 patients, 180 were referred to them

by the local hospital. Provide a 99% confidence interval for all the patients who are referred

to this facility by the hospital.

a. 0.9 ± 0.013*0.021

b. 0.9 ± 2.575*0.021

c. 0.9 ± 2.601*0.021

d. 0.9 ± 2.601*0.00045

e. 0.9 ± 2.575*0.00045

Answer questions 12 – 15 based on the following.

A supermarket wants to test whether the mean weight of the cans of peas sold by a particular

maker equals 24 oz. It chooses a random sample of 16 cans and finds that the sample mean is

23.3 oz and the sample standard deviation is 0.4 oz. Your job is to test, at the 5% level of

significance, whether or not the mean weight equals 24 oz.

12. What are the null and alternative hypotheses?

a. Ho: µ = 24, Ha: µ ≠ 24

b. Ho: µ ≤ 24, Ha: µ > 24

c. Ho: µ ≥ 24, Ha: µ < 24

d. Ho: µ = 23.3, Ha: µ ≠ 23.3

13. Compute the p-value. When computing two-tailed p-values, remember to use the 2p

approach!

a. 0.00000214

b. 0.0503

c. 0.00000428

d. 0.1006

e. 0.2012

14. What is your conclusion?

a. Reject the null hypothesis at the 5% level

b. Fail to reject the null hypothesis at the 5% level

c. Reject the null hypothesis at the 2.5% level

d. Fail to reject the null hypothesis at the 2.5% level

e. None of these responses

15. Compute the power of the test when µ = 24.1.

a. 0.0037

b. 0.1480

c. 0.8520

d. 0.8557

e. 0.9963

Answer questions 16 – 17 based on the following.

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in

statistics today and those enrolled five years ago. A sample of final examination scores from

students enrolled today and from students enrolled five years ago was taken. You are given the

following information:

Today Five Years Ago

x̅ 82 88

σ

2

112.5 54

n 45 36

16. The 95% confidence interval for the difference between the two population means (Today –

Five Years Ago) is

a. -9.92 to -2.08

b. -3.08 to 3.92

c. -13.84 to -1.16

d. -24.77 to 12.23

e. 2.08 to 9.92

17. The statistics teacher wishes to test, using a two-tailed approach, the hypothesis of no

difference between the population mean scores using a 5% level of significance. The p-value

associated with this test is: When computing two-tailed p-values, remember to use the 2p

approach!

a. 0.0013

b. 0.0026

c. 0.4987

d. 0.9987

18. A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces. A 95%

confidence interval estimate for the variance of the population is

a. 0.2313 to 0.8533

b. 0.2224 to 0.7924

c. 0.0889 to 0.3169

d. 0.0925 to 0.3413

Answer questions 19 – 20 based on the following.

The standard deviation of the ages of a sample of 16 executives from northern states was 8.2

years, while the standard deviation of the ages of a sample of 25 executives from southern states

was 12.8 years. At α = 0.10, test to see if there is any difference in the standard deviations of the

ages of all northern and southern executives.

19. Compute the p-value associated with this test. When computing two-tailed p-values, remember

to use the 2p approach!

a. 0.0498

b. 0.0772

c. 0.1873

d. 0.3746

20. What is the probability of rejecting the null hypothesis when it is true?

a. 1%

b. 5%

c. 10%

d. None of these responses

Answer questions 21 – 23 based on the following.

Among 1,000 managers with degrees in business administration, the following data have been

accumulated as to their fields of concentration:

Position in Management

Major Top Management Middle Management

Management 300 200

Marketing 200 0

Accounting 100 200

Test, using α = 0.01, to determine if their position in management is independent of their major.

21. What is your test statistic?

a. -0.11

b. 25,600

c. 222.22

d. 14.91

22. Compute the critical value.

a. 0.02

b. 0.00

c. 4.61

d. 9.21

e. 16.81

23. What is your conclusion?

a. Reject the null at the 1% level

b. Fail to reject the null at the 1% level

c. Reject the null at the 0.5% level

d. Fail to reject the null at the 0.5% level

Answer questions 24 – 26 based on the following.

In order to compare the life expectancies of three different brands of printers, 8 printers of each

brand were randomly selected. Information regarding the 3 brands is shown below.

Brand A Brand B Brand C

Average Life (Months) 62 52 60

Sample Variance 36 25 49

At the 5% level of significance, test to see whether the mean life is the same across these brands.

24. Compute the p-value associated with your test statistic. When computing two-tailed p-values,

remember to use the 2p approach!

a. 0.0081

b. 0.0162

c. 0.0213

d. 0.0426

e. 0.1499

25. Compute Fisher’s LSD using Bonferroni’s adjusted α (set αEW = 0.05).

a. 5.211

b. 6.298

c. 7.848

d. 23.790

e. 51.244

26. Fisher’s LSD procedure suggests that µA __ µB, µB __ µC, and µA __ µC.

a. >, >, >

b. <, <, <

c. =, =, =

d. >, <, =

e. <, >, =

Johns Hopkins University Statistics Problem Set