Question

using the given table data to confidence interval of the requested level. x = 97, n = 226, confidence level =99%

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 97 / 226 = 0.429

1 - = 1 - 0.429 = 0.571

Z/2 = 2.576

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

= 2.576 * (((0.429 * 0.571) / 226)

Margin of error = E = 0.085

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.429 - 0.085 < p < 0.429 + 0.085

0.344 < p < 0.514

The 99% confidence interval for the population proportion p is : 0.344 , 0.514