Question

Several students were tested for reaction times​ (in thousandths of a​ second) using their right and left hands.​ (Each value is the elapsed time between the release of a strip of paper and the instant that it is caught by the​ subject.) Results from five of the students are included in the graph to the right. Use a 0.02 significance level to test the claim that there is no difference between the reaction times of the right and left hands.

Right Hand: 124, 118, 149, 183, 199

Left Hand: 144, 148, 174, 215, 225

Answer 1

Solution:

Here, we have to use paired t test for the difference between population means. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: there is no difference between the reaction times of the right and left hands.

Alternative hypothesis: H_a: there is a difference between the reaction times of the right and left hands.

H₀: µ_d = 0 versus H_a: µ_d ≠ 0

This is a two tailed test.

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

Dbar = -26.6

S_d = 4.6690

n = 5

df = n – 1 = 4

α = 0.02

Critical values = - 3.7469 and 3.7469

(by using t-table)

Test statistic is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (-26.6 - 0)/[ 4.6690/sqrt(5)]

t = -12.7391

P-value = 0.0002

(by using t-table)

P-value < α = 0.02

So, we reject the null hypothesis

There is insufficient evidence to conclude that there is no difference between the reaction times of the right and left hands.