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Intro to Statistics and Computing In Economics Spring 2016
Econ 2810 Intro to Statistics and Computing In Economics Spring 2016
Problem Set 3
Out: March 15 Due: April 7
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 = 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
Construct a 95% confidence interval for the diﬀerence, 1 2, in each of the following situations: n1 = 400; ˆ1 = 0:65; n2 = 400; ˆ2 = 0:58 n1 = 180; ˆ1 = 0:31; n2 = 250; ˆ2 = 0:25 n1 = 100; ˆ1 = 0:46; n2 = 120; ˆ2 = 0:61 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 400twoyear owners of model 1 is contacted, and a sample of 500 twoyear 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 = 0:10
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
1
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