Question

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals 500 comma x equals 350 comma 95 % confidence nothingless thanpless than nothing ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

n = 500

x = 350

Point estimate = sample proportion = = x / n = 350 / 500 = 0.70

1 - = 1 - 0.70 = 0.30

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = Z 0.025 = 1.96

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

= 1.96 * (((0. 70 * 0.30 ) / 500 )

= 0.040

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.70 - 0.040 < p < 0.70 + 0.040

0.660 < p < 0.740