Suppose We Wish to Construct a Confidence Interval for a Population

question 35

Multiple Choice

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: $$E = z _ { \alpha } / 2 \sqrt { \frac { \hat { p q } } { n } } \sqrt { \frac { N - n } { N - 1 } }$$
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 $N = 410$ . In a random sample of 89 students, selected without replacement, there are 10 left handers.

• A) \(0.057 < p < 0.167\)
• B) \(0.070 < \mathrm { p } < 0.155\)
• C) \(0.064 < p < 0.161\)
• D) \(0.074 < p < 0.150\)

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