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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
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
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
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
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.
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