Question

In a sample of 112 residences, 69 had reduced their water consumption. If we were to construct a 95% confidence interval for the proportion of residents who reduced their water consumption. What is our margin of error for a 95% confidence interval? Round to 3 decimal places.

Answer 1

Solution :

Given that,

n = 112

x = 69

Point estimate = sample proportion = = x / n = 69/112=0.616

1 -   = 1- 0.616 =0.384

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 (((0.616*.384) / 112)

E = 0.090