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Five subjects' IQ scores were measured before taking a "smarticle pill" and after. The following were the results:
IQ Before IQ After
105.2 114.3
114.86 117.0
71.64 93.7
76.16 97.2
83.61 90.0
a) Using the paired t-test, is there a significant difference between the before and after scores? Use the p-value method:
b) Now use the pooled t-test for independent samples to test whether there is a significant difference between the mean of the two columns. Assume equal variances and use the p-value method:
c) Compare the two outcomes. You should have rejected the hypotheses in one method and failed to reject the null hypothesis in the other. Obviously, these are two different conclusions and only one of them is correct. Which method and conclusion is correct and why?
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