Question

A survey of 540 citizens found that 331 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval?

Answer 1

Solution :

Given that,

n = 540

x = 331

= x / n = 331 / 540 = 0.613

1 - = 1 - 0.613 = 0.387

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

Z= Z_0.05 = 1.645

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

= 1.96 * (((0.613 * 0.387) / 540)

= 0.035

A 95% confidence interval for population proportion p is ,

- E = 0.613 - 0.035 = 0.578

The lower limit of the interval = 0.578