Question

Using traditional methods it takes 110.0 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 50 students and observed that they had a mean of 111.0 hours. Assume the variance is known to be 16.00. Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Step 1 of 5: Enter the hypotheses: Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Enter the decision rule. Step 5 of 5: Enter the conclusion.

Answer 1

Ans.

Step1:  

, it take 110 hrs to receive a basic driving license.

, it does not take 110 hrs to receive a basic driving license.

Step 2:

It is a two-tailed test.

As in the question it is mention that a new license technique effect differently on the hours to receive driving license, there is nowhere in question mention that this new technique increase or decrease the hours to receive a basic driving license.

Also when we write a , in a alternate hypothesis, it does mean that we are doing a two-tailed test.

Step 3:

Now we have to calculate the test statistic for our hypothesis in order to reject or FTR(fail to reject) our .

The for we use for this is :

It tells us that

now using a t-table for two tailed we need to find the value for, significance level , with degree of freedom(df=n-1).

If we find

Then we are FTR(fail to reject) .

Then we reject the , which we found the evidence that is likely to be true.

Using t-table we found for and for for two tail is:

So we found that our is less than our

i.e.,   1.768<2.021

Step 4:

As we find out that So we are FTR(fail to reject) our Null Hypothesis.

It implies that we not have evidence to believe that the Alternate hypotheis is true and the new Computer Aided Instruction(CAI) method does not have any effect in the hours that it take to receive a basic driving license.