9 Hypothesis Testing

Section 9.7 Exercises

CLARIFYING THE CONCEPTS

Question 9.352

1. Explain what a Type II error is. (p. 565)

9.7.1

A Type II error is not rejecting when is false.

Question 9.353

2. Describe what is. (p. 565)

Question 9.354

3. In words, what do we mean by the power of a hypothesis test? (p. 567)

9.7.3

The probability of rejecting when is false.

Question 9.355

4. How do we calculate the power of a test? (p. 567)

PRACTICING THE TECHNIQUES

CHECK IT OUT!

To do	Check out	Topic
Exercises 5–16	Example 34	Calculating , the probability of a Type II error
Exercises 17–28	Example 35	Power of a hypothesis test
Exercises 29–30	Example 36	Power curve

For Exercises 5–16, assume that the conditions for performing the test are met.

For Exercises 5–16, do the following:

Calculate the value or values of .
Draw a normal curve, centered at , with the value or values of indicated.
Calculate , the probability of a Type II error for that value of . Shade the corresponding area under the normal curve.

Question 9.356

9.7.5

(a) 51.024

(b)

(c) 0.5120

Question 9.357

Question 9.358

9.7.7

(a) 51.024

(b)

(c) 0.0068

Question 9.359

Question 9.360

9.7.9

(a) 51.024

(b)

(c) TI-83/84: 0.0000003353

Question 9.361

10.

Question 9.362

11.

9.7.11

(a) 96.71

(b)

(c) 0.3613

Question 9.363

12.

Question 9.364

13.

9.7.13

(a) 96.71

(b)

(c) 0.0093

Question 9.365

14.

Question 9.366

15.

9.7.15

(a) 96.71

(b)

(c) 0.000006658

Question 9.367

16.

For Exercises 17–28, calculate the power of the hypothesis test for the indicated exercise.

Question 9.368

17. Exercise 5

9.7.17

0.4880

Question 9.369

18. Exercise 6

Question 9.370

19. Exercise 7

9.7.19

0.9932

Question 9.371

20. Exercise 8

Question 9.372

21. Exercise 9

9.7.21

0.9999996647

Question 9.373

22. Exercise 10

Question 9.374

23. Exercise 11

9.7.23

0.6387

Question 9.375

24. Exercise 12

Question 9.376

25. Exercise 13

9.7.25

0.9907

Question 9.377

26. Exercise 14

Question 9.378

27. Exercise 15

9.7.27

0.999993342

Question 9.379

28. Exercise 16

Question 9.380

29. Refer to Exercises 17–22. Construct the power curve for the given values of .

9.7.29

Question 9.381

30. Refer to Exercises 23–28. Construct the power curve for the given values of .

APPLYING THE CONCEPTS

Question 9.382

31. Stock Market. The Statistical Abstract of the United States reports that the mean daily number of shares traded on the New York Stock Exchange in 2009 was 2.9 billion. Let this value represent the hypothesized population mean, and assume that the population standard deviation equals 0.7 billion shares. Suppose that we have a random sample of 36 days from the present year, and we are interested in testing whether the population mean daily number of shares traded has increased, using level of significance .

Describe what a Type II error would mean in the context of this problem.
What is the probability of making a Type II error when the actual mean number of shares traded equals the following values?
1. 3.0 billion
2. 3.1 billion
3. 3.2 billion
4. 3.3 billion
Calculate the power of the hypothesis test for the values of given in (b).
Construct the power curve for the values of given in (b).

9.7.31

(a) Concluding that the population mean daily number of shares traded equals 2.9 billion shares when, in reality, it has increased from 2.9 billion shares.

(b) and (c)

		Probability of Type 11 error: β	Power of Test:
(i)	3.0 billion
(ii)	3.1 billion
(iii)	3.2 billion
(iv)	3.3 billion

(d)

570

Question 9.383

32. Credit Scores in Georgia. According to CreditReport.com, the mean credit score in Georgia in 2014 was 668. Suppose we have a recent random sample of 900 credit scores in Georgia, and assume that the population standard deviation is 150. We are interested in testing using level of significance whether the population mean credit score in Georgia has decreased since that time.

Describe what a Type II error would mean in the context of this problem.
What is the probability of making a Type II error when the actual mean credit score takes the following values?
1. 650
2. 645
3. 640
4. 635
Calculate the power of the hypothesis test for the values of given in (b).
Construct the power curve for the values of given in (b).

Question 9.384

33. Accountants' Salaries. According to Salary.com, the mean salary for entry-level accountants in 2010 was $41,560. Let this value represent the hypothesized population mean, and assume that the population standard deviation equals $5000. Suppose we have a recent random sample of 100 entry-level accountants and want to test, using level of significance , whether the population mean salary has changed since 2010.

Describe what a Type II error would mean in the context of this problem.
What is the probability of making a Type II error when the actual mean salary takes the following values?
1. $42,000
2. $43,000
3. $44,000
4. $45,000
Calculate the power of the hypothesis test for the values of given in (b).
Construct the power curve for the values of given in (b).

9.7.33

(a) Concluding that the population mean salary for accountants is equal to $41,560 when, in reality, it has changed from $41,560.

(b) and (c)

	Probability of Type 11 error: β	Power of Test: 1 – β
(i) $42,000
(ii) $43,000
(iii) $44,000
(iv) $45,000

(d)

Question 9.385

34. Price of Milk. The U.S. Bureau of Labor Statistics reports that the mean price for a gallon of milk in June 2014 was $3.63. Suppose that we have a random sample taken this year of 400 gallons of milk, and assume that the population standard deviation equals $1.00. We want to conduct a hypothesis test, using level of significance , to investigate if the population mean price of milk this year has increased.

Describe what a Type II error would mean in the context of this problem.
What is the probability of making a Type II error when the actual mean price takes the following values?
1. $3.70
2. $3.90
3. $4.10
4. $4.30
Calculate the power of the hypothesis test for the values of given in (b).
Construct the power curve for the values of given in (b).