Question

In a sample of 124 residences, 73 had reduced their water consumption. If we to construct a 95% confidence interval for the proportion of residents who reduced their water consumption. What is our point estimate for the proportion of residents who reduced their water consumption? Round to 3 decimal places.

Answer 1

Solution :

Given that,

n = 124

x = 73

Point estimate = sample proportion = = x / n = 73/124=0.589

1 -   = 1- 0.589 =0.411

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 (((0.589*0.411) / 124)

E = 0.087

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.589-0.087 < p < 0.589+0.087

0.502< p < 0.676

The 95% confidence interval for the population proportion p is : 0.502, 0.676