Question

Use the normal distribution to find a confidence interval for a difference in proportions given the relevant sample results. Assume the results come from random samples. A 95% confidence interval for given that with and with Give the best estimate for , the margin of error, and the confidence interval. Round your answer for the best estimate to two decimal places and round your answers for the margin of error and the confidence interval to three decimal places. Best estimate : Enter your answer; Best estimate Margin of error : Enter your answer; Margin of error Confidence interval : Enter your answer; Confidence interval, value 1 to Enter your answer; Confidence interval, value 2

p1-p2 given that p1=0.76 with n1=570 and p2=0.61 with n2=230

Answer 1

Solution :

Given that,

= 0.76

1- = 0.24

= 0.61

1 - = 0.39

At 95% confidence level the z is ,

Z_/2 = 1.96

95% confidence interval for p₁ - p₂ is ,

( - )   Z_/2  * [(1- ) / n₁ + (1 - ) / n₂]

(0.76 - 0.61)   1.96 * [(0.76 * 0.24) / + (0.61 * 0.39) / 230]

0.15 0.072

0.078 < p₁ - p₂ < 0.222

(0.078 , 0.222)