Question

Using traditional methods, it takes 104104 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 100100 students and observed that they had a mean of 105105 hours. Assume the standard deviation is known to be 55. A level of significance of 0.050.05 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?

Answer 1

Answer with explanation:

Let
`\mu` be the population mean.

By considering the given information , we have

Null hypothesis :
`H_0: \mu=104`

Alternative hypothesis :
`H_0: \mu\\eq104`

Since alternative hypothesis is two-tailed , so the test is a two-tailed test.

Given : n=100 ;
`\overline{x}=105` ;
`s=55`

Test statistic:
`z=\frac{\overline{x}-\mu}{(s)/(√(n))}`

i.e.
`z=(105-104)/((55)/(√(100)))`

`=0.181818181818\approx0.18`

By using the standard normal distribution table for z , we have

P-value for two tailed test :
`2P(Z>|z|)=2(1-P(Z<|z|))`

`=2(1-P(z<0.18))=2(1-0.5714237)=0.8571526`

Since , the P-value is greater than the significance level of
`\alpha=0.05` , it means we do not have evidence to reject the null hypothesis.

Hence, we conclude that we do not have enough evidence to support the claim that the technique performs differently than the traditional method.