Question

A simple random sample of 800 elements generates a sample proportion of 0.70.

Provide a 90% confidence interval for the population proportion. (round to two decimal places) [Answer , Answer]

Provide a 99% confidence interval for the population proportion. (round to two decimal places) [Answer , Answer]

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.70

1 - = 1 - 0.70 = 0.3

Z/2 = 1.645

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

= 1.645 * (((0.70 * 0.3) / 800)

= 0.03

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.70 - 0.03 < p < 0.70 + 0.03

0.67 < p < 0.73

The 95% confidence interval for the population proportion p is : 0.67 , 0.73

Point estimate = sample proportion = = 0.70

1 - = 1 - 0.47 = 0.3

Z/2 = 2.576

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

= 2.576 * (((0.70 * 0.3) / 800)

= 0.04

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.70 - 0.04 < p < 0.70 + 0.04

0.66 < p < 0.74

The 99% confidence interval for the population proportion p is : 0.66 , 0.74