Question

Q 4       A PSYCHIATRIST WANTS TO DETERMINE IF A SMALL AMOUNT OF ALCOHOL DECREASES THE REACTION TIME IN ADULTS. THE MEAN REACTION TIME FOR A SPECIFIED TEST IS 0.20 SECONDS. A SAMPLE OF 64 PEOPLE WERE GIVEN A SMALL AMOUNT OF ALCOHOL AND THEIR REACTION TIME AVERAGED 0.17 SECONDS. DOES THIS SAMPLE RESULT SUPPORT THE PSYCHIATRIST'S HYPOTHESIS? USE MEAN = 0.20 SECONDS, STANDARD ERROR = 0.01, ALPHA = 0.01                              
                                      
                                      
                                      
                                      
                                      
                                      
       PLEASE FORMULATE THE NULL AND ALTERNATIVE HYPOTHESES                              
       THE SAMPLE IS NORMALLY DISTRIBUTED, LIST THE CRITICAL VALUE AND SOLVE                              
                                      

Answer 1

Step 1:

Ho: = 0.20

Ha: < 0.20

Null hypothesis states that the mean reaction time for a test is 0.20

Alternative hypothesis states that the mean reaction time for a test is less than 0.20

Step 2: Test statistics

n = 64

sample mean = 0.17

SE = 0.01

z = -3.00

Step 3:

level of significance - 0.01

Critical Value of Z (Left Tailed): - 2.33

As the z stat ( -3.00) falls in the rejection area, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that mean reaction time for a test is less than 0.20