Question

Thirty five percent of adult Americans are regular voters. A random sample of 350 adults in a medium size college town were surveyed, and it was found that 155were regular voters. Estimate the true proportion with 95% confidence and comment on your results.Write a conclusion for the confidence interval.Round to 3 decimalplaces.

Answer 1

Solution :

Given that,

n = 350

x = 155

Point estimate = sample proportion = = x / n = 155 / 350 = 0.443

1 - = 1 - 0.443 = 0.557

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

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

= 1.96 (((0.443 * 0.557) / 350)

= 0.052

At 95% confidence interval for population proportion p is ,

- E < p < + E

0.443 - 0.052 < p < 0.443 + 0.052

0.391 < p < 0.495

( 0.391 , 0.495 )

The 95% confidence interval for the true population proportion p is : ( 0.391 , 0.495 )