Question

Using traditional methods it takes 105.0 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 on 290 students and observed that they had a mean of 106.0 hours. Assume the standard deviation is known to be 7.0 . Is there evidence at the 0.02 level that the technique performs differently than the traditional method? Step 4 of 5: Enter the decision rule. Step 5 of 5: Enter the conclusion.

Answer 1

Solution:

Given:

Sample Size = n = 290

Sample mean =

Population Mean =

Population standard deviation =

Level of significance =

We have to test: A new license training method using Computer Aided Instruction (CAI) technique performs differently than the traditional method.

Since this is non-directional statement, this is two tailed test.

Thus we use following steps:

Step 1) State H0 and H1:

Vs

Step 2) Test statistic:

Step 3) Find z critical value:

Level of significance =

Since this is two tailed, test find

Area =

Thus look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.

Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03

Thus Z_c = 2.33

Since this is two tailed test, z critical values are: (-2.33 , 2.33)

Step 4) Decision Rule:

Reject null hypothesis H0, if | z | test statistic value > 2.33 , otherwise we fail to reject H0.

Since z test statistic value = 2.43 > 2.33 , we reject null hypothesis H0.

Step 5) Conclusion: Since we have rejected null hypothesis H0, there is sufficient evidence to conclude that: A new license training method using Computer Aided Instruction (CAI) technique performs differently than the traditional method.