Question

To test whether alcohol has an effect on reaction time, 10 subjects were given reaction-tests on two different days. Each subject drank a glass of liquid containing alcohol before one of the two tests and a glass of liquid not containing alcohol before the other one. The order of presentation was randomised independently for each subject. The reaction times in 1/10 second are given in the table below.

Subject	1	2	3	4	5	6	7	8	9	10
With Alcohol	4.7	5.1	5.8	4.8	6.0	4.4	5.5	6.1	5.6	4.9
Without Alcohol	3.9	4.0	4.4	3.0	5.1	4.1	5.5	6.8	4.7	4.6

(a) Carry out the appropriate test at 5% level of significance and check whether there is significant evidence that alcohol has an effect on reaction time.

(b) Give the p-value of the test. Do you come to the same conclusion by using p-value? Explain. (DETAIL ANSWER PLEASE!)

Answer 1

a)

Difference Scores Calculations

Treatment 1

N₁: 10
df₁ = N - 1 = 10 - 1 = 9
M₁: 5.29
SS₁: 3.13
s²₁ = SS₁/(N - 1) = 3.13/(10-1) = 0.35


Treatment 2

N₂: 10
df₂ = N - 1 = 10 - 1 = 9
M₂: 4.61
SS₂: 9.61
s²₂ = SS₂/(N - 1) = 9.61/(10-1) = 1.07


T-value Calculation

s²_p = ((df₁/(df₁ + df₂)) * s²₁) + ((df₂/(df₂ + df₂)) * s²₂) = ((9/18) * 0.35) + ((9/18) * 1.07) = 0.71

s²_M1 = s²_p/N₁ = 0.71/10 = 0.07
s²_M2 = s²_p/N₂ = 0.71/10 = 0.07

t = (M₁ - M₂)/√(s²_M1 + s²_M2) = 0.68/√0.14 = 1.81

The t-value is 1.80751. The p-value is .087426.

b) p > 0.05, null is not rejected. So, no effect