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 1 2 3 4 5 mean std. dev. Sober (S) 109 132 248 155 202 169.2 55.9 After Wine (AW) 141 128 290 174 260 198.6 72.5 Diff. (d = S − AW) −32 4 −42 −19 −58 −29.4 23.5 Assume that all necessary 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.

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

using minitab>stat>basic stat>paired t

we have

Paired T-Test and CI: Sober, After wine

Paired T for Sober - After wine

N Mean StDev SE Mean
Sober 5 169.2 55.9 25.0
After wine 5 198.6 72.5 32.4
Difference 5 -29.4 23.5 10.5

95% upper bound for mean difference: -7.0
T-Test of mean difference = 0 (vs < 0): T-Value = -2.80 P-Value = 0.024

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

(B) between 0.02 and 0.025.