Answer to Question #205020 in Statistics and Probability for marwa

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.