Question

11.2a

A substance abuse researcher wants to know whether reaction time is increased by frequent alcohol use. He randomly selects 92 alcoholics and finds that their mean reaction time (in ms) equals 439.1. Reaction times to the stimulus in the general population are distributed normally with a mean equal to 445 and a standard deviation equal to 58.5 . Is there sufficient evidence to conclude that reaction times of alcoholics are higher than those of the general population? Use a significance level of 0.1

Step 1 of 5 :  

State the Null and Alternative Hypotheses for this scenario.

(All five answers are needed, please.)

Answer 1

Solution :

= 439.1

=445

=58.5

n = 92

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 439.1

H_a :     439.1

Test statistic = z

= ( - ) / / n

= (445 - 439.1) /58.5 / 92

= 0.967

P(z > ) = 1 - P(z < 0.967 ) = 0.3334

P-value = 0.3334

= 0.01

P-value > 0.01

it is concluded that the null hypothesis Ho is not rejected.

Therefore, there is not enough evidence to claim that the population mean \muμ is different than 439.1, at the 0.01 significance level.