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

Category: Education, General
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