1. A college is expecting an entering freshman class of 700 students. The mean score on a test of writing skills for 100 freshmen attending one of several college orientation sessions is 86. The σM for the writing test is 1.5 points.
a. uld the admissions officer make for the writing skills of the entire incoming freshman class?
b. In constructing an interval estimate for the writing skills of the entire incoming freshman class, what score will fall in the center of the interval?
c. The admissions officer can be 95% confident that the mean writing skills score for the entire incoming class falls between which two values?
d. If the admissions officer were willing to be only 90% confident, would the confidence interval be larger or smaller? Why?
e. If only 60 of the 100 students who attended the orientation session took the writing skills test, would the confidence interval be larger or smaller? Why?
2. Carmine reads an article that says that male college students study less than female college students. Carmine wonders if this is really so. He asks 20 randomly selected students-10 males and 10 females-from his coed dorm to record their study times for a period of 4 weeks. Here are the students' average weekly study times, to the nearest half-hour:
| Males |
Females |
| 13.5 |
15.5 |
| 6.5 |
10.0 |
| 8.0 |
10.0 |
| 14.5 |
7.0 |
| 12.5 |
13.0 |
| 16.0 |
12.5 |
| 12.0 |
11.0 |
| 9.5 |
8.5 |
| 7.0 |
8.0 |
| 11.5 |
13.0 |
a. Is the research hypothesis in this study directional or no directional?
b. State the research hypothesis.
c. Calculate t and compare it with the tabled critical t at the .05 a level. Can you reject the null hypothesis?
d. Do you think these samples are representative of all college males and females? To what populations can Carmine rightfully infer the results?