Question

8) According to the US Census Bureau, 43% of men who worked at home were college graduates. In a sample of 499 women who worked at home, 173 were college grads. What is the upper bound for 99% confidence interval for the proportion of women who work at home who are college grads? Round to 3 decimal places.

9) A medical researcher wants to construct a 99% confidence interval for the proportion of knee replacement surgeries result in complications. An article suggested that approximately 8% of such operations result in complications. Using this estimate, what sample size is needed so the confidence interval will have a margin of error of 0.077? Write only an integer as your answer.

Answer 1

8. The statistical software output for this problem is:

Hence,

Upper bound of 99% confidence interval = 0.402

9. p = 0.08

q = 1 - p = 1 - 0.08 = 0.92

For 99% confidence, z = 2.576

E = 0.077

Hence,

Sample size required

n = 83