Question

Consider the following results for independent samples taken from two populations. Sample 1 Sample 2 ni = 400 n2= 300 P1= 0.44 P2= 0.36 a. What is the point estimate of the difference between the two population proportions (to 2 decimals)? b. Develop a 90% confidence interval for the difference between the two population proportions (to 4 decimals). Use z-table. to c. Develop a 95% confidence interval for the difference between the two population proportions (to 4 decimals). Use z-table. to

Answer 1

a)

point estimate is  

P1 - P2

= 0.44 - 0.36 = 0.08

b)

CI = P1 - P2 -ZC P1(1 – Ô1) Ni Ộ2 (1 – ô2) ,P1 N2 Ô2 +26 V P1(1 – P1) Ni Ô2 (1 – P2) N2 0.44(1 – 0.44) = 0.44 – 0.36 – 1.645 x + 0.36(1 – 0.36 300 ,0.44 – 0.36 + 1.645 x 0.44(1 – 0.44) 400 0.36(1 – 0.36) 300 400 = (0.019,0.141)

So, the answer is [0.0183, 0.1417]

c)

CI = - 2c1 P1(1 - P1) Ni + Ô2 (1 – Ô2) ,1 – P2 + ZcV N2 P1(1 - P1) Ni + P2(1 - P2) N2 0.44 – 0.36 – 1.96 x 0.44(1 – 0.44) 400 + 0.36(1 – 0.36) -,0.44 – 0.36 + 1.96 x 300 0.44(1 – 0.44) 400 + 0.36(1 – 0.36) 300 = (0.007,0.153)

So, the answer is [0.0065, 0.1535]

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