Question

The numbers of successes and the sample sizes for independent simple random samples from two populations...

The numbers of successes and the sample sizes for independent simple random samples from two populations are x 1equals32​, n 1equals40​, x 2equals10​, n 2equals20. a. Use the​ two-proportions plus-four​ z-interval procedure to find an​ 95% confidence interval for the difference between the two populations proportions. b. Compare your result with the result of a​ two-proportion z-interval​ procedure, if finding such a confidence interval is appropriate.

Homework Answers

Answer #1

X1 = 32

n1 = 40

X2 = 10

n2 = 20

a. the two proportion plus four z-interval

p1 = (X1 +1)/(n1+2)

= (32+1)/(40+2)

= 0.7857

p2= (X2+1)/(n2+2)

= (10+1)/(20+2)

= 0.5

Z = 1.96 at 95 % confidence level for two tail test

so, (0.7857-0.5) 1.96 * 0.124

= 0.2857 0.24304

= 0.04266 to 0.52874

b. two proportion z-interval

P1 hat = 32/40 = 0.8

p2 hat = 0.5

n1 = 40

n2 = 20

z = 1.96

so, (0.80-0.50) 1.96 * 0.12845

= 0.3 0.251762

= 0.048238 to 0.551762

so, both confidence interval are same so, confidence interval is appropriate of two-proportions plus-four​ z-interval

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