Question

Using traditional methods it takes 11.1 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 26 students and observed that they had a mean of 11.6 hours with a standard deviation of 1.6. Is there evidence at the 0.1 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal.

State the null and alternative hypotheses.

Find the P-value for the hypothesis test. Round your answer to four decimal places.

Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

Given that,

Population mean = = 11.1

Sample mean = = 11.6

Sample standard deviation = s = 1.6

Sample size = n = 26

Level of significance = = 0.1

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 11.1

Ha: 11.1

The test statistics,

t = ( - )/ (s/)

= ( 11.6 - 11.6 ) / ( 1.6 / 26)

= 1.593

p-value = 0.1236

The p-value is p = 0.1236 > 0.1 it is concluded that the null hypothesis is fail to reject.

Conclusion :

It is concluded that the null hypothesis Ho is fail to reject. Therefore, there is not enough evidence to claim that the technique

performs differently than the traditional method, at the 0.1 significance level.