Question

Construct a confidence interval of the population proportion at the given level of confidence.

x equals 160 comma n equals 200 comma 95 % confidencex=160, n=200, 95% confidence

The lower bound is

nothing.

The upper bound is

nothing.

?(Round to three decimal places as? needed.)

Answer 1

Solution :

Given that,

n = 200

x = 160

= x / n = 160 / 200 = 0.800

1 - = 1 - 0.800 = 0.200

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 * (((0.800 * 0.200) / 200)

= 0.055

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.800 - 0.055 < p < 0.800 + 0.055

0.745 < p < 0.855

The lower bound id 0.745 .

The upper bound is 0.855 .