Question

You wish to see if there is a difference between the average score of boys and girls on the math SOL. A random sample of 195 boys had an average score of 444.34 with a standard deviation of 45.65. A random sample of 202 girls had an average score of 452.64 and a standard deviation of 37.75.

A: Verify the assumptions.

B: State the 95% confidence interval for the difference of the average SOL scores.

C: Does this interval shows, at 95% confidence, that the averages are different.

Answer 1

A) Assumptions:

• The samples are random and independent.
• The sample size is reasonably large
• The distribution is normal distributed.

B)

For Sample 1 : x̅1 = 444.34, s1 = 45.65, n1 = 195

For Sample 2 : x̅2 = 452.64, s2 = 37.75, n2 = 202

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 376.3715 = 376

95% Confidence interval for the difference :

At α = 0.05 and df = 376, two tailed critical value, t_c = T.INV.2T(0.05, 376) = 1.966

Lower Bound = (x̅1 - x̅2) - t_c*√(s1²/n1 +s2²/n2) = (444.34 - 452.64) - 1.966*√(45.65²/195 + 37.75²/202) = -16.582

Upper Bound = (x̅1 - x̅2) + t_c*√(s1²/n1 +s2²/n2) = (444.34 - 452.64) + 1.966*√(45.65²/195 + 37.75²/202) = -0.018

C.

As the confidence interval do not contain 0. so we Reject the null hypothesis.

There is enough evidence to conclude that the averages are different at 0.95 confidence level.