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t-test
t-test is frequently used to test differences in means for two datasets.

Independent data set

A clinical trial tests for the effect of a cholesterol lowering drug gives the following results:

placebo   drug
200        205
215        220
225        220
230        225
210        220
210        205
200        205
220        195
           200
           195
           190
H0 The null hypothesis: the mean cholesterol level for the drug-treated group = mean cholesterol level for the placebo group.
Ha The alternative hypothesis: the mean cholesterol level for the drug-treated group < mean cholesterol level for the placebo group.
Using one-tailed t-test for independent samples, we find p = 0.12. The null hypothesis cannot be rejected in favor of the alternative hypothesis, i.e., the drug is not effective.

Dependent data set (paired)

A clinical trial tests for the effect of a cholesterol lowering drug gives the following results:

Before     After
treatment  treatment
200        205
215        220
225        220
230        225
210        220
210        205
200        205
220        195
195        200
205        195
200        190
H0 The null hypothesis: the mean cholesterol level is the same after drug treatment.
Ha The alternative hypothesis: the mean cholesterol level is lower after drug treatment.
Using one-tailed t-test for dependent (paired) samples, we find p = 0.20. The null hypothesis cannot be rejected in favor of the alternative hypothesis, i.e., the drug is not effective.

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