Question

If n = 420 and ˆpp^ (p-hat) = 0.5, construct a 90% confidence interval.

Give your answers to three decimals

? < p < ?

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.5

1 - = 1 - 0.5 = 0.5

Z_/2 = 1.645

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

= 1.645 * (((0.5 * 0.5) / 420)

Margin of error = E = 0.040

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.5 - 0.040 < p < 0.5 + 0.040

0.460 < p < 0.540