Question

A substance abuse researcher wants to know whether reaction time is increased by frequent alcohol use. He randomly selects 52 alcoholics and finds that their mean reaction time (in ms) equals 401.4. Reaction times to the stimulus in the general population are distributed normally with a mean equal to 395 and a standard deviation equal to 80 . Is there sufficient evidence to conclude that reaction times of alcoholics are higher than those of the general population? Use a significance level of 0.01

Step 4 of 5 :  

Enter the decision rule.

Answer 1

Solution :

= 395

= 401.4

= 80

n = 52

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 395

H_a : > 395

The significance level is α=0.01

and the critical value for a right-tailed test is t_c​=2.402.

Test statistic = z

= ( - ) / / n

= (401.4- 395) /80 / 52

= 0.577

p(Z > 0.577) = 1-P (Z < 0.577 ) = 0.2833

P-value = 0.2833

= 0.01

p= 0.2833 ≥ 0.01, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to claim that the population mean μ is greater than 395, at the 0.01 significance level.