Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 25, x = 10; 95% confidence.

Answer 1

Solution :

Given that,

n = 25

x = 10

Point estimate = sample proportion = = x / n = 10 / 25 = 0.400

1 - = 1 - 0.400 = 0.600

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 * (((0.400 * 0.600) / 25)

= 0.192

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.400 - 0.192 < p < 0.400 + 0.192

0.208 < p < 0.592

(0.208 , 0.592)