Question

A trial is conducted 300 times with 75 successes. With a confidence level of 95% find p and q (proportion)

Answer 1

Solution :

Given that,

n = 300

x = 75

Point estimate = sample proportion = = x / n = 75 / 300 = 0.25

1 - = 1 - 0.25 = 0.75

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.25 * 0.75) / 300)

= 0.049

A 95% confidence interval for population proportion p is ,

± E   

= 0.25  ± 0.049

= ( 0.201, 0.299 )