Methods of computation and quantitative ability

A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Which is this person's stronger ability:
verbal or quantitative? Explain your answer to a person who has never had a course in statistics.

You are conducting a survey at a college with 800 students, 50 faculty members, and 150 administrative staff members. Each of these 1,000 individuals has a single listing in the campus phone directory. Suppose you were to cut up the directory and pull out one listing at random to contact. What is the probability it would be (a) a student, (b) a faculty member,(c) an administrative staff member, (d) a faculty or administrative staff member, and (e) anyone except an administrative staff member? (f) Explain your answers to someone who has never had a course in statistics.

A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, and 36 square feet. (a) Figure the mean and standard deviation for the governors and for the CEOs. (b) Explain what you have done to a person who has never had a course in statistics. (c) Note the ways in which the means and standard
deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations' CEOs in general.

Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, what should the experimenter conclude? (a) Use the steps of hypothesis testing, (b) sketch the distributions involved, and (c) explain your answer to someone who is familiar with the t test for a single sample, but not with the t test for independent means.