Question

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals 550 comma x equals 440 comma 95 % confidence nothingless thanpless than nothing ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

n =550

x = 440

= x / n =440 /550 = 0.8

1 - = 1 - 0.8 = 0.2

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 * (((0.8(0.2)) / 550) = 0.033

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.8- 0.033 < p < 0.8+ 0.033

0.767 < p < 0.833

The 95% confidence interval for the population proportion p is : ( 0.767, 0.833)