Question

In random, independent samples of 400 adults and 325 teenagers who watched a certain television show, 244 adults and 159 teens indicated that they liked the show. Let P, be the proportion of all adults watching the show who liked it, and let P, be the proportion of all teens watching the show who liked it. Find a 95% confidence interval for P -P2. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval? xs ?

Answer 1

Here we have: X1 = 244 x2 = 159 n = 400 n2 = 325 a = 1-0.95 = 0.05 (95% confidence level) Sample proportion: X1 244 == =— 400 = 0.61 s 159 = 0.489 n2 325 Critical value: Zcrit= Za 12 = 20.05/2 = +1.96

Confidence interval: (P1-P2) = (P1-P2) +zc* * P1(1-1) P2(1-02) n2 (P1-P2) = (0.61-0.489) + 1.96 * 0.61(1-0.61) 400 0.489(1-0.489) 325 ✓ (P1-P2) = 0.121 + 0.072 -0.049 < (P1-P2) <0.193 Lower limit = 0.049 Upper limit = 0.193