A college is expecting an entering freshman class of 700. The sex ratio of the incoming class is exactly 350 women and 350 men. The mean score on a test of writing skills for 70 incoming female freshmen attending one of several college orientation sessions is 84. The mean score for 70 incoming. Male freshmen on the same writing test at the same orientation sessions is 78. The 0"w^w? for the writing test is 2.15 points.
a. What point estimate should the admissions officer make for the difference in writing score between women and men in the entire incoming freshman class?
b. In constructing an interval estimate for the difference in writing score between men and women in the entire incoming freshman class, what difference score will fall in the center of the interval?
c. The admissions officer can be 95% confident that the difference in writing score for men and women in the entire incoming freshman class falls between which two values?
d. If the admissions officer were willing to be only 90% confident, would the confi-dence interval be larger or smaller? Why?
e. If only 50 of the 70 women and 50 of the 70 men who attended the orientation session took the writing skills test, would the confidence interval be larger or smaller? Why?