Question

1. A college has been given a sizable grant: enough to build either a new library or gymnasium. But, as there is only money enough to build one facility, the president wants to ask students which one they feel is in greater need of renovation. Suppose there are 500 male students and 400 female students in the school.

1. What is the population under study? (2 points)
2. The president wants to randomly ask 50% of the students. How many students would this be? (2 points)
3. Now the president wants to keep the correct proportion of female to male students in the sample. What type of sampling method would be used here? How many girls would be selected? (4 points)
4. What is the level of measurement for the students’ response? (2 points)

2. The following are two hypothetical statements by American politicians.

Politician A: “Our economy is in the crapper! Thirty states had falling incomes last year.”

Politician B: “Our economy is showing appreciable gains: Seventy percent of Americans had rising incomes last year.”

1. Suppose both statements are true. How to reconcile these two seemingly contradicting statements? (4 points)
2. What lessons can we learn about descriptive statistics from this example? (4 points)

3. On a Saturday evening your father and mother take you out for dinner. There are 7 other customers in the restaurant. Their ages are as following: 44, 56, 25, 40, 32, 34, 38.

1. Write down the ages for your father, mother and you. (2 points)
2. Construct a stem-and-leaf graph for the age of all the customersin the restaurant. (3 points)
3. Comment on the shape of the whole data set. (3 points)
4. Compute the mean, the median and the mode of the whole data set. (6 points)
5. Compute the 40^th percentile of the whole data set. (3 points)

Answer 1

Question 1:

(a) The population under study is students in the school.

(b) Number of students = 0.5*(500 + 400) = 450

(c) The two-proportion z-test is appropriate here.

Girls = (400/900)*450 = 200

(d) The level of measurement for the students’ response is nominal.