Question

Construct a confidence interval for p 1 minus p 2p1−p2 at the given level of confidence. x1=357​, n1=502​, x2=427427​, n2=579, 99​% confidence

Answer 1

Solution :

1 = x1/n1 = 357/502 = 0.7112 ,

2 = x2 / n2 = 427 / 579 = 0.7375

99% confidence interval for p1 - p2 is

1 - 2 - Z/2 Sqrt(1(1-1)/n1 + 2(1-2)/n2) < p1 - p2 < 1 - 2 + Z/2 Sqrt(1(1-1)/n1 + 2(1-2)/n2)

(0.7112 - 0.7375) +- 2.5758 * Sqrt( 0.7112*0.2888 / 502 + 0.7375 * 0.2625 / 579)

-0.09653537 < p1 - p2 < 0.0439353791

-0.097 < p1-p2 < 0.044

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