Echinacea is widely used as an herbal remedy for the common cold, but does it work?  In a double-blind experiment, healthy volunteers agreed to be exposed to common-cold-causing rhinovirus type 39 and have their symptoms monitored.  The volunteers were randomly assigned to take either a placebo or an echinacea supplement daily from 7 days before till 5 days after viral exposure.  A symptom score was recorded for each subject over the 5 days following exposure, with higher scores indicating more severe symptoms. The published results reported the mean ± SEM for both groups as 13.21 ± 1.91 (echinacea) and 15.05 ± 1.43 (placebo).

The two-sample t statistic for x1 − x2 was t = −0.771.  You can draw a conclusion from this t without using a table and even without knowing the sizes of the samples.  Specify your null and alternative hypotheses. H 0 : μE = μP vs. Ha : μE ≠ μP
H 0 : μE = μP vs. Ha : μE > μP
H 0 : μE = μP vs. Ha : μE < μP
H 0 : μE − μP = 0 vs. Ha : μE − μP ≠ 0

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