Question

Use the normal distribution to find a confidence interval for a proportion p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample. A 95% confidence interval for p given that p Overscript ^ EndScripts equals 0.42 and n equals 450. Round your answer for the best point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places.

best point estimate ?

MOE?

95% CI?

Answer 1

Solution :

Given that,

n =450

Point estimate= = 0.42

1 - = 1 - 042 = 0.58

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.42 * 0.58) / 450)

= 0.046

Margin of error = E = 0.046

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.42 - 0.046 < p < 0.42 + 0.046

0.374 < p < 0.466

(0.374 , 0.466)