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 n = 400 observations from a binomial population with x = 111 successes.

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Answer 1

Solution :

Given that,

n = 400

x = 111

Point estimate = sample proportion = = x / n = 111/400=0.278

1 -   = 1- 0.278=0.722

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 *((0.278*0.722) /400 )

E = 0.037

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.278-0.037 < p < 0.278+0.037

__0.241____to___0.315___