Question

Find the necessary confidence interval for the binomial proportion p. (Round your answers to three decimal places.)

A 90% confidence interval for p, based on a random sample of 985 trials of a binomial experiment which produced 592 successes.

Answer 1

Solution :

Given that,

n = 985

x = 592

Point estimate = sample proportion = = x / n = 592/985=0.601

1 -   = 1-0.601=0.399

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.601*0.399) /985 )

E = 0.026

A 90% confidence interval p is ,

- E < p < + E

0.601-0.026 < p < 0.601+0.026

0.575< p < 0.627

(0.575 , 0.627)