Question

A 95% confidence interval for p is given as (0.43,0.77). How large was the sample used to construct this​ interval? (n)

Answer 1

Solution :

Given that

confidence interval =  (0.43,0.77)

Point estimate = = (Lower confidence interval + Upper confidence interval ) / 2

Point estimate = = (0.43 + 0.77) / 2 = 0.60

Margin of error = E = Upper confidence interval - = 0.77 - 0.60 = 0.17

= 0.60

1 - = 1 - 0.60 = 0.40

margin of error = E = 0.17

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = 1.96

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96 / 0.17)² * 0.60 * 0.40

= 31.90

sample size = n = 32