Econ 2810 Intro to Statistics and Computing In Economics Problem Set 3

1. A manufacturer of paper products wants to compare the variation in daily production levels at two paper mills. Independent random samples of days are selected from each mill, and the production levels (in units) are recorded. The data are show in the table below. Do the data provided provide evidence to indicate a difference in the population variances at the two paper mills. Use α = 0.10.

Mill 1: 34 18 28 21 40 23 29

          25 10 38 32 22 22

Mill 2: 31 13 27 19 22 18 23 22 21

        18 15 24 13 19 18 19 23 13

2. Construct a 95% confidence interval for the difference, ρ1 − ρ2, in each of the following situations:

a. n1 = 400, ρˆ1 = 0.65, n2 = 400, ρˆ2 = 0.58

b. n1 = 180, ρˆ1 = 0.31, n2 = 250, ρˆ2 = 0.25

c. n1 = 100, ρˆ1 = 0.46, n2 = 120, ρˆ2 = 0.61

3. A consumer advocacy group wants to determine whether there is a difference between proportions of the two leading automobile models that need major repairs within 2 years of purchase. A sample of 400 two-year owners of model 1 is contacted, and a sample of 500 two-year owners of model 2 is contacted. The numbers X1 and X2 of owners who report that their cars needed major repairs within the first two years are 53 and 78, respectively. Test the null hypothesis that no difference exists between the proportions in population 1 and 2 needing major repairs against the alternative that a difference does exist. Use α = 0.10

4. Suppose you select independent random samples of five female and five male high school seniors and record their SAT scores. The data is shown below. Based on this data, calculate the sum of squares for groups (SSG), error (SSE), and total (SST).

Table 1: SAT scores for High School Students

Females Males

539         490

560        520

590        550

620         580

650         610