Question

Question 5 View Policies Current Attempt in Progress Use the normal distribution to find a confidence interval for a difference in proportions Pu - P2 given the relevant sample results. Assume the results come from random samples. A 99% confidence interval for Pi - P2 given counts of 117 yes out of 170 sampled for Group 1 and 149 yes out 180 sampled for Group 2 Give the best estimate for Pi-P2, the margin of error, and the confidence interval. Round your answers to three decimal places. Best estimate : i Margin of error: i Confidence interval:

Answer 1

solution:-

group 1

x1 = 117 , n1 = 170

p1 = x1/n1 = 117/170 = 0.688

group 2

x2 = 149 , n2 = 180

p2 = x2/n2 = 149/180 = 0.828

Best estimate = p1-p2

= 0.688 - 0.828

= -0.14

margin of error

the value of 99% confidence from z table is 2.576

margin of error formula

=> z * sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

=> 2.576 * sqrt((0.688*(1-0.688)/170) + (0.828*(1-0.828)/180))

=> 0.117

confidence interval formula

=> Best estimate +/- margin of error

=> -0.14 +/- 0.117

=> (-0.257 to -0.023)