1. Consider a scenario where you have two samples. Sample 1 contains 30 observat
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Question
1. Consider a scenario where you have two samples. Sample 1 contains 30 observations, has the sample average value of 37 and the sample standard deviation of 2.5. Sample 2 contains 20 observations, has the sample average of 39 and the sample standard deviation of 2.0.
Based on this information, please conduct a 90% significance test for the equality of the two population means. Note that we don't know the population standard deviations but we can assume that they are equal
2.Consider a scenario where you have two samples. Sample 1 contains 30 observations, has the sample average value of 37 and the sample standard deviation of 2.5. Sample 2 contains 20 observations, has the sample average of 39 and the sample standard deviation of 2.0. Assume that we don't know the population standard deviations but we can assume that they are equal.
Which of the following tests would fail to reject the null hypothesis that the two population means are equal?
Explanation / Answer
1.) Hypothesis:
H0: µ1 - µ2 = 0
H1: µ1 - µ2 0
x1 = 37
x2 = 39
n1 = 30
n2 = 20
s1 = 2.5
s2 = 2
SE = sqrt[ (s12/n1) + (s22/n2) ]
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
t = [ (x1 - x2) - d ] / SE
SE = 0.639
DF = 60.61
d = 0
t = -3.12
P-value = 0.003
0.003 < 0.01
Hence, we can reject the null hypothesis.
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