The sample size needed to estimate the difference between two population proport

Question

The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 - a can be found as follows: in the expression E = z_a/2 squareroot P1q1/n_1 + P2q2/n_2 replace n_1 and n_2 by n (assuming both samples have the same size) and replace each of P_1, q_1. P_2 and q_2 by 0.5 (because their values are not known). Then solve for n. Use this approach to find the size of each sample if you want to estimate the difference between the proportions of men and women who plan to vote in the next presidential election. Assume that you want 99% confidence that your error is no more than 0.06. 359 755 922 535

Explanation / Answer

E= z*sqrt(p1q1/n1+p2q2/n2)

For 99%, z=2.576

0.06 =2.576 sqrt(0.5*0.5/n+0.5*0.5/n)

Squaring both sides,

0.062 =2.5762 *(2*0.25/n)

n = 2.5762 *0.5/0.062

=921.63

Sample size required =922 ( rounded up)

Answer : C) 922

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.