Question

Of 250 adults selected randomly from one town, 72 of them smoke. Construct a 95% confidence interval for the true percentage of all adults in the town that smoke

Answer 1

Solution : -

Given that,

n = 250

x = 72

Point estimate = sample proportion = = x / n = 72 / 250 = 0.288

1 - = 1 - 0.288 = 0.712

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 ((( 0.288 * 0.712 ) / 250 )

= 0.056

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.288 - 0.056 < p < 0.288 + 0.056

0.232 < p < 0.344

23.2%  < p < 34.4%

The 95% confidence interval for the true percentage of all adults in the town that smoke is : - 23.2%  < p < 34.4%