Question

Using traditional methods, it takes 108 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 280 students and observed that they had a mean of 109 hours. Assume the standard deviation is known to be 6. A level of significance of 0.02 will be used to determine if the technique performs differently than the traditional method. Is there sufficient evidence to support the claim that the technique performs differently than the traditional method? What is the conclusion?

Answer 1

Solution:

Given:

Using traditional methods, it takes 108 hours to receive a basic driving license.

That is:

A new license training method using Computer Aided Instruction (CAI) has been proposed.

Sample size = n = 280

Sample mean =

Population Standard deviation =

level of significance = = 0.02

We have to test if the new technique performs differently than the traditional method or not.

thus this is two tailed test.

Step 1) State H0 and H1:

Vs

Step 2) Test statistic:

Step 3) Find z critical values:

level of significance = = 0.02

Since this is two tailed test , find: Area =

look in z table for area = 0.0100 or its closest area and find z value.

Area 0.0099 is closest to 0.0100 and it corresponds to -2.3 and 0.03

thus z critical value = -2.33

thus critical values are: ( -2.33 , 2.33 )

Step 4) Decision rule:

Reject null hypothesis H0 ,if z  test statistic value < z critical value=-2.33 or z  test statistic value > z critical value=2.33, otherwise we fail to reject H0.

Since z test statistic value= > > z critical value=2.33, we reject null hypothesis H0 at 0.02 level of significance.

Step 5) Conclusion:

At 0.02 level of significance, there is sufficient evidence to support the claim that the technique performs differently than the traditional method