Question

Using traditional methods it takes 92 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 93 hours. Assume the population variance is known to be 36. Is there evidence at the 0.050.05 level that the technique lengthens the training time?

Step 2 of 6 :  

Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Solution:
Given in the question
The claim is that the technique lengthens the training time.
Null hypothesis H0: = 92 hours
Alternate hypothesis Ha: > 92 hours
Sample mean(Xbar) = 93
Population variance = 36
So Population standard deviation () = 6
No. of sample n = 70
So test statistic value can be calculated as
Test statistic = (Xbar - )//sqrt(n) = (93 - 92)/6/sqrt(70) = 1.39
Here we will Z test sample size is greater than 30 and the population standard deviation is also known. So p-value from Z table can be found as this is a right-tailed test so P-value = 0.0816
Here at alpha = 0.05, we can are failed to reject the null hypothesis as the p-value is greater than alpha value so we dont have significant evidence to support the claim that the technique lengthens the training time.