Question:

Suppose that two random samples of sizes n1, and n2 are selected without replacement from two binomial populations with means = μ1=n1p1,   μ2=n2p2,\mu_1= n_1p_1, \,\,\,\mu_2= n_2p_2, and variances σ12=n1p1q!,   σ22=n2p2q2σ_1 ^2 = n_1p_1q_!, \,\,\,σ_2^2 = n_2p_2q_2 , respectively. Let the difference of sample proportions P1\overline{P_1} and P2\overline{P_2} approximate a normal distribution with mean (p1p2p_1 - p_2). Then the standard deviation of the difference of sample proportions  P1\overline{P_1} and P2\overline{P_2} , is

Updated On: Oct 1, 2024
  • (p1q1n1)(N1n1N11)+(p2q2n2)(N2n2N21)\sqrt{(\frac{p_1q_1}{n_1})(\frac{N_1-n_1}{N_1-1})+ (\frac{p_2q_2}{n_2})(\frac{N_2-n_2}{N_2-1})}
  • (p1qqn1)+(p2q2n@)\sqrt{(\frac{p_1q_q}{n_1})+(\frac{p_2q_2}{n_@})}
  • (p1q1p2q2n1+n2)\sqrt{(\frac{p_1q_1-p_2q_2}{n_1+n2}})
  • (p1q1n1+n2)(N1n1N11)+(p2q2n1+n2)(N2n2N21)\sqrt{(\frac{p_1q_1}{n_1+n_2})(\frac{N_1-n_1}{N_1-1})+ (\frac{p_2q_2}{n_1+n_2})(\frac{N_2-n_2}{N_2-1})}
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The Correct Option is A

Solution and Explanation

The correct option is (A): (p1q1n1)(N1n1N11)+(p2q2n2)(N2n2N21)\sqrt{(\frac{p_1q_1}{n_1})(\frac{N_1-n_1}{N_1-1})+ (\frac{p_2q_2}{n_2})(\frac{N_2-n_2}{N_2-1})}
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