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Do online students perform differently than students in a traditional classroom? Last semester there were 100...

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Statistics

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

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Answer & Explanation Solved by verified expert
3.6 Ratings (420 Votes)

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
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