Question

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.

Answer 1

(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.

Solution:

i)

ii.)yes, data indicate practical significance.

iii) P-value is very less, we reject null hypothesis.

Ans:Yes, data data indicate statistical significance.

b.)

(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.

i.)

Null hypothesis: P₁ = P₂

Alternative hypothesis: P₁ ≠ P₂

ii.)

yes, data indicate practical significance.

iii.)there is statistically significant difference between two proportions.

Ans:Yes, data data indicate statistical significance.

c.)

i.)Null hypothesis: P₁ = P₂

Alternative hypothesis: P₁ ≠ P₂

_ii.)

yes, data indicate practical significance.

iii.) as p-value is very large i,e p-value > 0.05

Ans:No the data is not statistical significance