Question

In a survey of 1000 U.S. adults, 700 think police officers should be required to wear body cameras while on duty.

a. Construct a 90% confidence interval for the proportion of all U.S. adults that think police officers should be required to wear body cameras while on duty.

b. Interpret your confidence interval.

Answer 1

Solution :

Given that,

n = 1000

x = 700

= x / n = 700 / 1000 = 0.700

1 - = 1 - 0.700 = 0.300

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.700 * 0.300) / 1000)

= 0.024

A 90% confidence interval for population proportion p is ,

- E < P < + E

0.700 - 0.024 < p < 0.700 + 0.024

0.676 < p < 0.724

(0.676 , 0.724)