Witte & Witte, 9e Page 1 of 4 Pages

Chapter 11

Chapter 11: More About Hypothesis Testing

Exercise 1

Each of the following statements indicates that the researcher will be using a one-tailed test. Specify the null and alternative for each situation.

a.  The national average on a test of aggressiveness is 50. A researcher wishes to determine whether, for individuals who have participated in aggression-reducing exercises, the average is less than 50.

b.  The average number of people attending a Protestant church service in 2003 was 89. An investigator wants to determine whether the average attendance is currently greater than 89. Source: http://www.barna.org/FlexPage.aspx?Page=Topic&TopicID=10

c.  The average amount of meat consumed in 2007 was 222 pounds per person. A researcher wants to find out if the average meat consumption has decreased in a city where the residents were encouraged to eat more fruits and vegetables. Source: http://www.hsus.org/farm/resources/pubs/stats_meat_consumption.html

d.  The average amount a couple typically spends on wedding rings is $1,575. A market researcher wants to find out if couples who reside in the Midwest spend, on average, more than $1,575. Source: http://honeymoons.about.com/cs/eurogen1/a/weddingstats.htm

e.  A study reported in September 2009 by Economist.com found that the average number of friends a Facebook user has is 120. A researcher wants to find out if the average for high school students is greater than 120. Source: http://www.economist.com/sciencetechnology/displayStory.cfm?story_id=13176775

Answers:

a.  H0:  ≥ 50

H1:  < 50

b.  H0:  ≤ 89

H1:  > 89

c.  H0:  ≥ 222

H1:  < 222

d.  H0:  ≤ $1,575

H1:  > $1,575

e.  H0:  ≤ 120

H1:  > 120

Exercise 2

For each of the following situations, indicate whether H0 should be retained or rejected.

a.  z = -1.92, two-tailed test,  = .05

b.  z = -1.92, one-tailed test, lower tail critical,  = .05

c.  z = 2.45, two-tailed test,  = .05

d.  z = 2.45, two-tailed test,  = .01

e.  z = -3.25, one-tailed test, upper tail critical,  = .05

f.  z = -1.77, one-tailed test, lower tailed critical,  = .05

g.  z = 2.16, one-tailed test, upper tailed critical,  = .01

Answers:

a.  Retain

b.  Reject

c.  Reject

d.  Retain

e.  Retain

f.  Reject

g.  Retain

Exercise 3

You are concerned with how well college-educated women in Wisconsin cope with divorce. You have reason to believe that they cope better than the general population. You sample 100 female college-educated Wisconsin residents who were divorced in the past six months and you have them take the Coping With Divorce survey. The CWD has a population mean of 48 and a population standard deviation of 12. High scores on the CWD indicate coping well whereas low scores on the CWD indicate coping poorly. The CWD mean of your sample comes out to be 50. Carry out a directional test with  equal to .05.

1.  What is the correct form of the null hypothesis?

a.  H0:  = 48

b.  H0:  ¹ 48

c.  H0:  ³ 48

d.  H0:  48

2.  What is the correct form of the alternative hypothesis?

a.  H1:  = 48

b.  H1:  ¹ 48

c.  H1:  > 48

d.  H1:  < 48

3.  What is the z critical value that will be used in the decision rule?

a.  1.65

b.  –1.65

c.  2.33

d.  –2.33

4.  Calculate z.

5.  What statistical decision should be made?

a.  Reject H0

b.  Retain H0

6.  On the basis of the results, would you conclude that college-educated Wisconsin females are different from the general population with respect to coping with divorce?

a.  Yes, they cope better.

b.  Yes, they cope less well.

c.  No evidence that they cope differently.

Answers:

1.  d

2.  c

3.  a

4.  1.67

5.  a

6.  a

Exercise 4

For each of the following situations, indicate whether the researcher has made a type I error, a type II error, or the correct decision.

a.  The researcher rejected the null hypothesis when, in fact, the null hypothesis is false.

b.  The researcher retained the null hypothesis when, in fact, the null hypothesis is false.

c.  The researcher rejected the null hypothesis when, in fact, the null hypothesis is true.

d.  The researcher rejected the null hypothesis when, in fact, the null hypothesis is false.

Answers:

a. Correct decision

b. Type II error

c. Type I error

d. Correct decision

Exercise 5

1.  A researcher sets alpha equal to .05 for a two-tailed test and estimates that statistical power is equal to .80. For this research situation:

a.  The type I error probability is equal to ___.

b.  The type II error probability is equal to ___.

2.  A researcher sets alpha equal to .05 for a one-tailed test and estimates that statistical power is equal to .75. For this research situation:

a.  The type I error probability is equal to ___.

b.  The Type II error probability is equal to ___.

3.  A researcher sets the type I error probability equal to .01 for a two-tailed test and estimates that the type II error probability is equal to .15. For this research situation:

a.   = ___.

b.   = ___.

c.  Statistical power = ___.

4.  A researcher sets the type I error probability equal to .05 for a one-tailed test and estimates that the type II error probability is equal to .32. For this research situation:

a.   = ___.

b.   = ___.

c.  Statistical power = ___.

Answers:

1.  a. .05; b. 1 - .80 = .20

2.  a. .05; b. 1 - .75 = .25

3.  a. .01; b. .15; c. 1 - .15 = .85

4.  al .05; b. .32; c. 1 - .32 = .68

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