Question

A New Orleans reproductive clinic reported 57 live births to 285 women under the age of 40 who had previously been unable to conceive.

1) What critical value is needed to find a 92% confidence interval for the true proportion of women who conceive after previously being unable to do so? Round final answer to two (2) decimal places.Find and interpret this 92% confidence interval, rounding the bounds/limits of the confidence interval to four (4) decimal places. Suppose a researcher at the New Orleans reproductive clinic above wants to establish a 5% margin of error in the study above. Using the answers you found for questions 1 and 2, and still using a 92% confidence level, what is the minimum sample size necessary to keep this 5% margin or error?

Answer #1

1) For 92% confidence interval, the critical value is
z^{*} = 1.75

= 57/285 = 0.2

The 92% confidence interval is

= 0.2 +/- 0.0415

= 0.1585, 0.2415

We are 92% confident that the true proportion of women who conceive after previously being unable to do so.

2) Margin of error = 0.05

Or, z^{*} * sqrt(p(1 - p)/n) = 0.05

Or, 1.75 * sqrt(0.2(1 - 0.2)/n) = 0.05

Or, n = (1.75 * sqrt(0.2 * 0.8)/0.05)^2

Or, n = 196

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