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

Step-by-step explanation:

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

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

$z=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

where , n= sample size

$\overline{x}$ = sample mean

$\mu$ = Population mean

$\sigma$ =Population standard deviation.

As per given we have,

n= 270

$\mu= 108$

$\overline{x}=107$

$\sigma^2=49\\\\\Rightarrow \sigma=\sqrt{49}=7$

Then, z-statistic  will be

$z=\dfrac{107-108}{\dfrac{7}{\sqrt{270}}}$    (Substitute all the values )

$\Rightarrow\ z=\dfrac{-1}{\dfrac{7}{16.4316767252}}$  

$\Rightarrow\ z=\dfrac{-1}{0.426006433614}$  

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

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