Question

The mean grade point average for statistical inference I course in a particular session is 2.45 with variance of 0.4761 it is believed that statistics majors have higher grade point average than the overall mean. A sample of 100 statistics major had a mean grade point average of 2.65. Test his claim at 1% level of significance

Answer 1

$H_0:\mu=2.45$ , majors have not higher grade point average than the overall mean

$H_a:\mu>2.45$ , majors have higher grade point average than the overall mean

$z=\frac{\overline{x}-\mu}{\sigma/\sqrt{n}}=\frac{2.65-2.45}{\sqrt{0.4761}/10}=2.90$

critical value:

$z_{crit}=2.576$

Since $z>z_{crit}$ , we have to reject the null hypothesis. Majors have higher grade point average than the overall mean.