A sociologist is studying the effect of having children within the first 2 years of marriage on the divorce rate.Using hospital birth records,she selects a simple random sample of 200 couples who had children within the first 2 years of marriage.Following up on these couples,she finds that 80 couples are divorced within 5 years.Let p = the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years.Suppose the sociologist wishes to test H₀: p = ⅓ versus H_a: p $\neq$ ⅓.At the 10% significance level,are the data statistically significant for testing these hypotheses? A)Yes B)No C)This cannot be determined from the information given.

Question

Quizplus · Accepted Answer

The sample proportion of couples who are divorced within 5 years is 80/200 = 0.4. To test the hypothesis at the 10% significance level, we compare the sample proportion to the hypothesized population proportion of 1/3 (approximately 0.333). The difference between the sample proportion (0.4) and the hypothesized proportion (0.333) is likely to be statistically significant, given the sample size of 200, indicating that the data provide enough evidence to reject the null hypothesis at the 10% significance level.

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