1 let the random variables x1 and x2 follow binomial, Ask an Expert

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1. Let the random variables X1 and X2 follow binomial distributions that have parameters n1 = 100, n2 = 75, Let x1 = 35 and x2 = 27 be observed values of X1 and X2. Let p1 and p2 be the true proportions. Determine an appropriate 95% con?dence interval for p1 - p2.

2. The following information is obtained from two independent samples selected from two populations.

n1 = 40 x1 = 28.4 s1 = 4.1
n2 = 32 x2 = 25.6 s2 = 4.5

(a) What is the maximum likelihood estimator of μ1 - μ2?

(b) Construct a 99% con?dence interval for μ1 - μ2.

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