Question

You want to find the proportion of residents in Richmond who support bringing a professional sports team to the area. Of the 98 people you survey, 43 of them would support a professional team. Create a 95% confidence interval for the proportion of all Richmond residents who would support a professional team. Please show the work so I can understand the math

Answer 1

Solution :

Given that,

n = 98

x = 43

= x / n = 43 / 98 = 0.439

1 - = 1 - 0.439 = 0.561

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.439 * 0.561) / 98)

= 0.098

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.439 - 0.098 < p < 0.439 + 0.098

0.341 < p < 0.537

(0.341 , 0.537)