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A random sample of 100 men produced a total of 25 who
Chapter 9, Problem 90E(choose chapter or problem)
A random sample of 100 men produced a total of 25 who favored a controversial local issue. An independent random sample of 100 women produced a total of 30 who favored the issue. Assume that \(p_M\) is the true underlying proportion of men who favor the issue and that \(p_W\) is the true underlying proportion of women who favor the issue. If it actually is true that \(p_{W}=p_{M}=p\), find the MLE of the common proportion p.
Questions & Answers
QUESTION:
A random sample of 100 men produced a total of 25 who favored a controversial local issue. An independent random sample of 100 women produced a total of 30 who favored the issue. Assume that \(p_M\) is the true underlying proportion of men who favor the issue and that \(p_W\) is the true underlying proportion of women who favor the issue. If it actually is true that \(p_{W}=p_{M}=p\), find the MLE of the common proportion p.
ANSWER:Step 1 of 3
Consider \(Y_{1}\) as the number of people in the sample who favored a controversial local issue among men.
Given,
\(Y_{1}=25\)
\(Y_{2}\) denotes the number of people in the sample who favored a controversial local issue among women.
Given,
\(Y_{2}=30\)