Never forget that even small effects can be statistically significant if the samples are large. Of 148 small businesses, 106 were headed by men and 42 were headed by women. During a three-year period, 15 of the men's businesses and 7 of the women's businesses failed. The proportions pˆ1 and pˆ2 of failures for businesses headed by women and businesses headed by men respectively, are?

The z test for the hypothesis that the same proportion of women's and men's business fail (using the two-sided alternative) has: ?

The sample proportions are quite close to each other and the test is very far for being significant.
Now suppose that the same sample proportions came from a sample 30 times as large. That is, 210 out of 1260 businesses headed by women and 450 out of 3180 businesses headed by men, fail.

A 95% confidence interval for the difference between the proportions of women?s and men?s businesses that fail, in the setting of (1) and (3) are,

What is the effect of larger samples on the confidence interval?