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

question 28

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 = 330. In a random sample of 86 students, selected without replacement, there are
8 left handers.

• A) 0.053 < p < 0.133
• B) 0.058 < p < 0.128
• C) 0.041 < p < 0.145
• D) 0.049 < p < 0.137

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