Question

In a random sample of 30 arthroscopic surgeries, 12% were unsuccessful. Find a 95% confidence interval for the proportion of arthroscopic surgeries in the population that were unsuccessful.

Answer 1

Sample size = n = 30

Sample proportion of surgeries that were unsuccessful = p = 12% = 0.12

Level of significance = = 1 - 0.95 = 0.05

Hence, the critical value of z for two tailed test at 0.05 level of significance = = 1.96

This can be obtained from the z table by finding the z for which area is approximately equal to 0.025 (as it is two tailed test so 0.025 area on both tails).

The 95% confidence interval for Population proportion of surgeries that were unsuccessful (P) is given by -

= [ 0.06, 0.18]