T-TEST PROBLEMS

Case 1

A famous nonverbal communication scholar believes that anxiety is an important variable in nonverbal behavior. On the basis of the assumption that anxious people have more energy than those who are calm, he hypothesizes that anxious people gesture more often while they talk than do calm people. He tests this hypothesis by randomly selecting five anxious people and five calm people (measured on a valid and reliable scale) from a university class. He tells each research participant to bring a friend to a laboratory where he videotapes 20 minutes of their conversation. He then counts the average number of gestures per minute made by each research participant. He obtains the following scores:

Anxious People Calm People

3 4 3 6 4 7 5 9 5 9

A. State the research hypothesis.

B. State the null hypothesis.

C. Is this a one-tailed or a two-tailed test?

D. What are the degrees of freedom?

E. If alpha is set at .05, what is the critical value needed for rejecting the null hypothesis?

F. What is the t-value?

G. Does the study support the research hypothesis?______________________________________________________________________________

Answers to t-test problem #1: (a) Anxious people gesture significantly more often while talking than calm people; (b) Anxious people do not differ from calm people in how often they gesture while talking; (c) one-tailed; (d) 8; (e) 1.86; (f) 2.86; yes, the t-value exceeds the critical value and warrants rejection of the null hypothesis.

Case 2

A clever undergraduate, Grace N. Poise, hypothesizes that people under 30 are more humorous than people over 30. She tests this hypothesis by randomly selecting 4 people over 30 from the telephone book and 4 people under 30 from university registration lists. She gives each research participant the Humorous Speech Scale, which measures humor on a Likert-type scale from 1 to 10. The scores are listed below.

People Under 30 People Over 30

6 57 6

10 29 3

A. State the research hypothesis.

B. State the null hypothesis.

C. Is this a one-tailed or a two-tailed test?

D. What are the degrees of freedom?

E. If alpha is set at .01, what is the critical value needed for rejecting the null hypothesis?

F. What is the t-value?

G. Was Ms. Poise's research hypothesis supported?______________________________________________________________________________

Answers to t-test problem #2: (a) People under 30 are more humorous than people over 30; (b) People under 30 do not differ from people over 30 in ability to be humorous; (c) one0-tailed; (d) 6; (e) 3.14); (f) 4.38; (g) yes