Question

A random sample of of 100 voters in a town is selected, and 24 are found to support an annexation suit. Find the 96% confidence interval for the fraction of the voting population favoring the suit.

Answer 1

Answer: 0.24 +/- 0.088 = (0.152, 0.328)

Explanation:

The point estimate p is given by;

p= 24/ 100 = 0.24

Z value for 96% confidence interval is 2.05

The solution for the given confidence interval is derived using the equation

p +/- z√(pq/n)

Where p = 0.24 q= 1-p = 0.76, n=100 z= 2.05

= 0.24 +/- 2.05√(0.24×0.76/100)

= 0.24 +/- 2.05(0.0427)

=0.24 +/- 0.088

= ( 0.152, 0.328)