Recall that small effects may be statistically significant if the samples are large. A study of small-business failures looked at 150 food-and-drink businesses. Of these, 104 were headed by men and 46 were headed by women. During
Recall that small effects may be statistically significant if the samples are large. A study of small-business failures looked at 150 food-and-drink businesses. Of these, 104 were headed by men and 46 were headed by women. During a three-year period, 13 of the men's businesses and 8 of the women's businesses failed.
Give the P-value for the z test of the hypothesis that the same proportion of women's and men's businesses fail. (Use the two-sided alternative.) The test is very far from being significant. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z=
p-value =
(b) Now suppose that the same sample proportions came from a sample of 30 times as large. That is, 240 out of 1380 business headed by women and 390 out of 3120 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in (a). Repeat the z test for the new data, and show that it is now more significant. (Round your test statistic to two decimal places and your P-value to four decimal places.)
p-value =
z=
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