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

Econ 2810 Intro to Statistics and Computing In Economics

Problem Set 3

Out: October 26

Fall 2016

Due: November 10

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 X1and X2of 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

560

590

620

650

1

490

520

550

580

610

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