Question

Using traditional methods, it takes 95 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 170 students and observed that they had a mean of 94 hours. Assume the variance is known to be 49 . A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.

Answer 1

To Test :-
H0 :- µ = 95
H1 :- µ ≠ 95

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 94 - 95 ) / ( 7 / √( 170 ))
Z = -1.86

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.01 /2 ) = 2.576
| Z | > Z( α/2 ) = 1.86 < 2.576
Result :- Fail to reject null hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.01 level of significance
P value = 2 * P ( Z > 1.86 ) = 2 * 1 - P ( Z < 1.8626 )
P value = 0.0625
Since 0.0625 > 0.01 ,hence we reject null hypothesis
Result :- We fail to reject null hypothesis