Question

Of 147 adults selected randomly in one town, it was found that 31 of them smoke. If we were to calculate a 95% confidence interval for the proportion of people in this town who smoke, what is the margin of error? Round to 3 decimal places.

Answer 1

Solution :

Given that,

n = 147

x = 31

Point estimate = sample proportion = = x / n = 31/147=0.211

1 -   = 1- 0.211 =0.789

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 (((0.211*0.789) /147 )

E = 0.066

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.211-0.066 < p <0.211+ 0.066

0.145< p < 0.277

The 95% confidence interval for the population proportion p is : 0.145, 0.277

Margin of error = E = 0.066