Given data for the final examination scores for two classes

Given data for the final examination scores for two classes in differential equations X: 78, 89, 81, 94, 60, 67, 51, 73, 90, 93, 81, 68, 45, 100, 60, 102, 95, 87, 85, 96, 77, 79, 55, 89, 86, 75, 85, 76, 95, 84, 69 and Y: 65, 95, 94, 72, 56, 87, 89, 28, 71, 78, 54, 93, 91, 68, 88, 90, 69, 78, 69, 91, 70 (a) Test the hypothesis H0: mu X = mu Y against the alternative H1: mu X > mu Y at the alpha = 0.10 significance level assuming X and Y are N (mu X, sigma^2 X) and N (mu Y, sigma^2 Y) where sigma^2 X = sigma^2 Y

Solution

Since p>0.1, we accept the null hypothesis.

Hypothesis Test: Independent Groups (t-test, pooled variance)
	x	y
	79.52	76.00	mean
	14.60	16.75	std. dev.
	31	21	n
		50	df
		3.516	difference (x - y)
		240.035	pooled variance
		15.493	pooled std. dev.
		4.379	standard error of difference
		0	hypothesized difference
		0.80	t
		.2129	p-value (one-tailed, upper)