Question

Using traditional methods, it takes 106 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 260 students and observed that they had a mean of 105hours. Assume the variance is known to be 49. A level of significance of 0.02 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places.

Enter the value of the test statistic.

Answer 1

The Z statistic test is done here to check the clam

The hypotheses are:

$Ho: \mu= 106$

$Ha: \mu\neq 106$

Rejection region:

Reject Ho if |Z_obs|>Z_0.01=2.326

Test Statistic:

$Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{105-106}{\frac{7}{\sqrt{256}}}=-2.3035$

p-Value:

P value associated with Z calculated value can be computed using Z statistic table or, by calculator as 0.02144

Conclusion:

Since |Z(obs)|<Z(0.01)=2.326 and the P value =0.02144>0.02( Level of Significance), we fail to reject the null hypothesis and conclude that at the 2 % level of significance there is insufficient evidence to support the claim of significantly different mean.