No Sweat labels. Sample proportions from Example 9.1 and the two-way table in Example 9.2 (page 494) report the same information in different ways. We saw in Chapter 8 (page 479) that the z statistic for the hypothesis of equal population proportions is z = 3.30 with P < 0.001.

(a) Find the chi-square statistic X2 for this two-way table and verify that it is equal

(up to roundoff error) to z2.

(b) Verify that the 0.001 critical value for chi-square with df = 1 (Table F) is the square of the 0.0005 critical value for the standard Normal distribution (Table D). The 0.0005 critical value corresponds to a P-value of 0.001 for the two-sided z test.

(c) Explain carefully why the two hypotheses H0: p1 = p2 (z test)

H0: no relation between gender and label use (X2 test)

say the same thing about the population.