Question

Using traditional methods it takes 91 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 70 students and observed that they had a mean of 92 hours. Assume the population variance is known to be 25. Is there evidence at the 0.02 level that the technique lengthens the training time?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Step 1

To Test :-
H0 :- µ = 91
H1 :- µ > 91

Step 2

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 92 - 91 ) / ( 5 / √( 70 ))
Z = 1.67

Step 3

The test is one-tailed.

Step 4

P value = P ( Z < 1.6733 ) = 0.0471
Looking for the value Z = 1.67 in standard normal table to find the P value

Step 5

Level of significance α = 0.02

Step 6

Reject null hypothesis if P value < α = 0.02 level of significance
Since 0.0471 > 0.02 ,hence we fail to reject null hypothesis
Result :- We fail to reject null hypothesis