Question

Do online students perform differently than students in a traditional classroom? Last semester there were 100 students registered for the online version of a statistics course, and 100 students registered for the traditional classroom. All students took the same final exam. Suppose the group of online students had a mean exam score of 75 with a standard deviation of 3. The classroom students had a mean score of 76 with a standard deviation of 4. Does the sample data provide evidence that there is a difference in the average exam scores between the two groups? Test the relevant hypotheses at a significant level of x = 0.05.

Show your work.

Answer 1

since sample size is large we can use z distribution

null hypothesis: Ho:μ1-μ2			=	0
Alternate hypothesis: Ha:μ1-μ2			≠	0
for 0.05 level with two tail test , critical z=				1.960
Decision rule : reject Ho if absolute value of test statistic |z|>1.96
	Online		traditional
x1            =	75.00	x2            =	76.00
n1           =	100	n2           =	100
σ1           =	3.00	σ2           =	4.00
std error σx1-x2=√(σ21/n1+σ22/n2)    =sqrt(3^2/100+4^2/100) =			0.500
test stat z =(x1-x2-Δo)/σx1-x2     =(75-76)/0.5 =			-2.00

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that there is a difference in the average exam scores between the two groups