Question

A mathematics test was given to 50girls and 75 boys.The girl made an average grade of 76 with an SD of 6 and the boys made an average grade of 82 with an SD of 2. Test whether there is any difference between the performance of boys and girls

Answer 1

$n_1 = 50 \\ n_2=75 \\ \bar{x_1}=75 \\ s_1=6 \\ \bar{x_2}= 82 \\ s_2=2 \\ H_0: \mu_1 = \mu_2 \\ H_1: \mu_1 ≠ \mu_2$

Test-statistic:

$Z = \frac{\bar{x_1} -\bar{x_2}}{\sqrt{ (s_1^2/n_1)+(s^2_2/n_2) }} \\ Z= \frac{75-82}{\sqrt{ (6^2/50) +(2^2/75) }} = -7.96$

Let use 5 % significant level.

Two-tailed test.

Reject H₀ if Z≤ -1.96 or Z≥1.96.

$Z= -7.96 < Z_{crit}= -1.96$

Reject H₀.

There is enough evidence to conclude that there is any difference between the performance of boys and girls at 5% significant level.