Question

Researchers are studying the impact of alcohol consumption on a person’s ability to perform a simple task. Five subjects complete a small puzzle while sober, and then again after drinking three glasses of wine. The times (in seconds) are shown below, as well as some summary statistics:

Subject

Sober (S) After Wine (AW)

1

2

3

4

5 mean 169.2 198.6

std. dev. 55.9 72.5

109 132 248 155 202 141 128 290 174 260

Di↵.(d=SAW) 32 4 42 19 58 29.4 23.5

Assume that all appropriate normality conditions are satisfied. We would like to conduct a hypothesis test to determine whether there is evidence that the true mean time to complete a puzzle is longer after consuming three glasses of wine.

26. What are the hypotheses for the appropriate test of significance?

(A) H0: μd =0vs.Ha: μd <0
(B) H0: μS =μAW vs.Ha: μS >μAW (C) H0: X ̄d =0vs.Ha: X ̄d <0
(D) H0: μd =0vs.Ha: μd >0
(E) H0: X ̄S = X ̄AW vs. Ha: X ̄S < X ̄AW

27. The P-value of the appropriate test of significance is:

(A) between 0.01 and 0.02. (B) between 0.02 and 0.025. (C) between 0.025 and 0.05. (D) between 0.05 and 0.10. (E) between 0.10 and 0.15.

Answer 1

Subject	Sober (S)	After Wine (AW)	d=S-AW
1	109	141	-32	-2.6	6.76
2	132	128	4	33.4	1115.56
3	248	290	-42	-12.6	158.76
4	155	174	-19	10.4	108.16
5	202	260	-58	-28.6	817.96
SUM =			-147		2207.2
MEAN =			-29.4

(B) P-value is between 0.02 and 0.025

NOTE: If u take d=AW-S

then hypothesis will changed

and, P-value remains between 0.02 and 0.025