Solve the Problem $$E = z _ { \alpha } / 2 \sqrt { \frac { \hat { p }\hat { q } } { n } } \sqrt { \frac { N - n } { N - 1 } }$$

Multiple Choice

Solve the problem.
-Suppose we wish to construct a confidence interval for a population proportion p. If we sample without replacement from a relatively small population of size N, the margin of error E is modified to include the finite population correction factor as follows: $$E = z _ { \alpha } / 2 \sqrt { \frac { \hat { p }\hat { q } } { n } } \sqrt { \frac { N - n } { N - 1 } }$$ Construct a 90% confidence interval for the proportion of students at a school who are left handed. The number of students at the school is N = 400. In a random sample of 82 students, selected without replacement, there are 11 left handers.

A) 0.091 < p < 0.177
B) 0.086 < p < 0.182
C) 0.072 < p < 0.196
D) 0.079 < p < 0.189