Question

An examination was given to two classes consisting of 40 and 50 students, respectively. In the first class the mean grade was 74 with a standard deviation of 8, while in the second class the mean grade was 78 with a standard deviation of 7. Is there a significant difference between the performance of the two classesat a level of significance of a. 0.05, b. 0.01? c. What is the P value of the test

Answer 1

We have that

$n_1 = 40$

$\bar x_1 = 74$

$s_1 = 8$

$n_2 = 50$

$\bar x_2 = 78$

$s_2 = 7$

Suppose that two classes from the population have the respective means $\mu_1$ and $\mu_2$ .

Thus we have

$H_0 : \mu_1=\mu_2$

$H_1 : \mu_1\ne\mu_2$

$s=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}=\sqrt{\frac{8^2}{40}+\frac{7^2}{50}}=1.606$

$z=\frac{x_1-x_2}{s}=\frac{74-78}{1.606}=-2.49$

Using calculator we get the p-value = 0.013

a) a = 0.05

Since z lies outside the interval (-1.96 to 1.96) it is significant. We reject the null hypothesis Ho. We are 95% confident to conclude that there is difference in the mean of two classes.

b) a = 0.01

Since z lies inside the interval (-2.57 to 2.57) it is not significant. We accept the null hypothesis Ho. We are 99% confident to conclude that there is no difference in the mean of two classes.