Question

In 1998, a San Diego reproductive clinic reported 59 births to 307 women under the age of 40 who had previously been unable to conceive. The clinic wants to cut the margin of error in half to improve the precision of success rate. How many patients’ result, n, must be used? Give your answer to as a whole integer. Hint: (i) The z - critical value for a 90% confidence interval is 1.645. (ii) Remember to always round up when reporting calculated values for sample sizes.

Answer 1

Given a San Diego reproductive clinic reported X = 59 births to n = 307 women under the age of 40 who had previously been unable to conceive.

Thus the sample proportion is calculated as:

Now we need to find the margin of error which is calculated as:

Also given the Zc at 90% confidence level is 1.645 thus the margin of error is calculated as:

E = 0.037

Now, The clinic wants to cut the margin of error in half to improve the precision of success rate, hence the new marrgin of error would be:

E = 0.037/2 = 0.0185

now based on this margin of error the minimum sample is calculated as:

Now to improve the precision of success rate 1227 patients’ result, must be used.