Mathematics Homework Help
STATS 230 Kwantlen Polytechnic University Test Statistic Hypothesis Practice
I’m working on a statistics question and need an explanation to help me learn.
20. It is claimed that an industrial safety program is effective in reducing the loss of working hours due to factory accidents. The following table shows data on the weekly loss of working hours due to accidents at six plants both before and after the safety program is instituted. Sample means and sample standard deviations for the two data sets are given in the last two columns.
|
Plant |
1 |
2 |
3 |
4 |
5 |
6 |
x¯ |
s |
|||
|
Before |
12 |
29 |
16 |
37 |
28 |
15 |
22.83 |
9.91 |
|||
|
After |
10 |
28 |
17 |
35 |
25 |
16 |
21.83 |
9.15 |
|||
|
Change = After – Before |
-2 |
-1 |
1 |
-2 |
-3 |
1 |
-1 |
1.67 |
|||
|
2 |
(a) What is the most appropriate alternative hypothesis to test this claim? A.H1 : µAfter − µBefore < 0 B.H1 : µAfter − µBefore > 0? C.H1 : µAfter − µBefore 6= 0? D.None of the above |
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2 |
(b) What is the most appropriate test for inference on the two population means? A.Paired t-test B.Independent pooled t-test C.Welch procedure D.F-test |
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2 |
(c) What is the value of the test statistic associated with testing H0 : µAfter − µBefore = 0 against the alternative selecting in part (a)? A. 0.18 B. 1.47 C. 2.07 D. -2.07 E. None of the above |
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2 |
(d) Suppose a test statistic of tobs = −2 was obsered for this experiment. What is the p-value associated with the upper-tailed alternative hypothesis: H0 : µAfter − µBefore = 0 H1 : µAfter − µBefore > 0 A. 0.95 < p < 0.975 B. 0.9 < p < 0.95 C.0.05 < p < 0.1 D.0.025 < p < 0.05 E.None of the above |
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2 |
(e) Regardless of what you answered for (b), which of the following lines of R code would conduct the pooled t-test for testing the hypotheses in (d)? You may assume the following vectors exist in your R environment. |
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before <- c(12,29,16,37,28,15) after <- c(10,28,17,35,25,16)
t.test(before, after, alternative = “greater”, paired = FALSE, var.equal=FALSE) # A
t.test(before~after, alternative = “greater”, paired = FALSE, var.equal=FALSE) # B
t.test(before, after, alternative = “greater”, paired = FALSE, var.equal=TRUE) # C
t.test(before, after, alternative = “greater”, paired = TRUE, var.equal=TRUE) # D
A. B. C. D. E. None of the above
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