(2) To obtain an estimate of the proportion p, of New York City residents who fol...

Solution :

Given that,

a) n = 1498

x = 773

Point estimate = sample proportion = = x / n = 773 / 1498 = 0.516

1 - = 1 - 0.516 = 0.484

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

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

= 1.96 (((0.516 * 0.484) / 1498)

= 0.025

A 95% confidence interval for population proportion p is ,

± E

= 0.516 ± 0.025

= ( 0.491, 0.541 )

b) margin of error = E = 0.01

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

= (1.96 / 0.01)² * 0.516 * 0.484

= 9594.16

sample size = n = 9595