Let's see how students and faculty compare on a basic statistical question. Zuckerman, Hodgins, Zuckerman, and Rosenthal (1993) surveyed 550 people and asked a number of ques- tions on statistical issues. In one question a reviewer warned a researcher that she had a high probability of a Type I error because she had a small sample size. The researcher disagreed. Participants were asked, "Was the researcher correct?" The proportions of respondents, parti- tioned among students, assistant professors, associate professors, and full professors, who sided with the researcher and the total number of respondents in each category were as follows:
|
|
Students
|
Assistant Professors
|
Associate Professors
|
Full Professors
|
|
Proportion
|
.59
|
.34
|
.43
|
.51
|
|
Sample Size
|
17
|
175
|
134
|
182
|
(Note: These data mean that 59% of the 17 students who responded sided with the researcher. When you calculate the actual obtained frequencies, round to the nearest whole person.)
(a) Who do you think was correct?
(b) What do these data tell you about differences among groups of respondents? (Note: The researcher was correct. Our tests are specifically designed to hold the probability of a Type I error at a, regardless of the sample size.)