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# A researcher wished to test the effect of the addition of extra calcium

on the 'tastiness' of yogurt. Sixty-two adult volunteers were randomly divided into two groups of 31 subjects each. Group 1 tasted yogurt containing the extra calcium. Group 2 tasted yogurt from the same batch as group 1 but without the added calcium. Both groups rated the flavor on a scale of 1 to 10, with 1 being 'very unpleasant' and 10 being 'very pleasant.' The mean rating for group 1 was 6.5 with a standard deviation of 1.5. The mean rating for group 2 was 7.0 with a standard deviation of 2.0. Let M1 and M2 represent the true mean ratings we would observe for the entire population represented by the volunteers if all of them tasted, respectively, the yogurt with and without added calcium.  Consider

Ho: M1 - M2 = 0
Ha: M1 - M2 &gt; 0

Assuming that there really is no difference in taste between the two yogurts, what is the probability that we would get as extreme or more extreme of a difference in sample statistics as what we got, just by random chance?