Question

Using traditional methods, it takes 108 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 270 students and observed that they had a mean of 107 hours. Assume the variance is known to be 49. A level of significance of 0.1 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

Answer: z= -2.35

Explanation:

When the population variation is know, then we calculate the z-statistic.

Formula to calculate the z-test statistic is given by :-

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

where , n= sample size

`\overline{x}` = sample mean

`\mu` = Population mean

`\sigma` =Population standard deviation.

As per given we have,

n= 270

`\mu= 108`

`\overline{x}=107`

`\sigma^2=49\\\\\Rightarrow \sigma=√(49)=7`

Then, z-statistic will be

`z=(107-108)/((7)/(√(270)))` (Substitute all the values )

`\Rightarrow\ z=(-1)/((7)/(16.4316767252))`

`\Rightarrow\ z=(-1)/(0.426006433614)`

`\Rightarrow\ z=-2.34738238931\approx-2.35`

Hence, the value of the test statistic= z= -2.35