# Answer in Statistics and Probability for marwa #205020

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

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_1nemu_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.