Question

4. Find a 95% confidence interval for the true proportion of all Alabamians favoring the new law. A sample of four hundred (400) Alabamians found that two-hundred thirty-five (235) of them favored the new law. Please write the final answer in interval notation.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 235 / 400 = 0.588

1 - = 1 - 0.588 = 0.412

Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.588 * 0.412) / 400)

= 0.048

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.588 - 0.048 < p < 0.588 + 0.048

(0.540 < p < 0.636)