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.
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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