Re: Hypothesis Testing Using T-Test
Hi,
By changing the fifth element you blow up the estimate for the standard deviation of G1, i.e. , from 1.05 to 2.53. This has more impact than the increase in the difference between µ1 and µ2, 1.35 and 2.02 respectively. So the p-values in the t-test increase!
Note that a t-test assumes that the measurements come from NORMAL distributions! When a Anderson-Darling test is performed on the measurements it can not be rejected that G1 and G2 come from a normal distribution. However after G1 is modified (to G1b) the pvalue of the Anderson-Darling test is 0.017 so it can be rejected that G1b comes from a normal distribution. Strictly speaking, you can not trust the results of a t-test anymore.
kind regards,
Paul Nommensen ■
Hypothesis testing using t-test
Dear friends,
could you please write the solutions to the question:
Consider the following sets of observations from two groups:
G1 = {-0.07, 0.48, -0.44, -1.45, 1.74, 0.23}
G2 = {-0.42, -0.52, -0.73, -1.75, -1.70, -1.12, -1.94, -1.81}
Assume that the measurements come from distributions that have equal but unknown variances, and potentially different means µ1 and µ2.
a) Use a t-test to test the null hypothesis that the underlying means of G1 and G2 are equal at a significance level of 5%;
H0: µ1=µ2.
b) Use a t-test to test the null hypothesis that the underlying mean of G1 is larger than that of G2 at a significance level of 5%;
H0: µ1>µ2.
c) Use a t-test to test the null hypothesis that the underlying mean of G1 is smaller than that of G2 at a significance level of 5%;
H0: µ1<µ2.
d) How do you suppose your results would change if the fifth element of G1 is changed from 1.74 to 5.74? Why? ■