5. For each of the following three cases, explain (i) the hypotheses with a plau

Question

5. For each of the following three cases, explain (i) the hypotheses with a plausible definition of p1 and p2, (ii) whether or not the data indicate practical significance (use common sense and/or general knowledge), and (iii) whether or not the data indicate statistical significance.

(a) A recent study of perfect pitch tested 2,700 students in American music conservatories. It found that 7% of non-Asian students and 32% of Asian students have perfect pitch. A two-sample Z-test of the difference in proportions resulted in a p-value of < 0.0001.

(b) In July 1974, the PEW Research Center selected a large sample of voters. Sixty-six percent of those interviewed disapproved of President Nixon. In July 2007, the same PEW Research Center selected a comparable sample. In this case, 64.5% of those interviewed expressed disapproval of President Bush. The researchers pointed out that the p-value for comparing the two sample results was 0.023.

(c) In a survey conducted in a statistics class at Boston College, students were asked their views on a number of social issues; 56% of the male students and 38% of the female students supported the death penalty. In a statistics lab, the students computed the corresponding p-value as 0.21

Explanation / Answer

(a) A recent study of perfect pitch tested 2,700 students in American music conservatories. It found that 7% of non-Asian students and 32% of Asian students have perfect pitch. A two-sample Z-test of the difference in proportions resulted in a p-value of < 0.0001.

since p value is very lower this is significant and we reject Ho

(b) In July 1974, the PEW Research Center selected a large sample of voters. Sixty-six percent of those interviewed disapproved of President Nixon. In July 2007, the same PEW Research Center selected a comparable sample. In this case, 64.5% of those interviewed expressed disapproval of President Bush. The researchers pointed out that the p-value for comparing the two sample results was 0.023.

p value is greater than 0.05 (alpha) so we fail to reject Ho and the test is not significant

(c) In a survey conducted in a statistics class at Boston College, students were asked their views on a number of social issues; 56% of the male students and 38% of the female students supported the death penalty. In a statistics lab, the students computed the corresponding p-value as 0.21

p value is greater than 0.05 (alpha) we fail to reject Ho and the test is not significant

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