Question

A 95% confidence interval for p is given as (0.27,0.53). How large was the sample used to construct this interval? n(Round up to the nearest observation.)

Answer 1

9Given  95% confidence interval for population proportion P is ( 0.27, 0.53)

ie lower limit = 0.27 upper limit = 0.53

then margin of error E = (Upper limit - Lower limit )/ 2

= (0.53- 0.27)/2

E = 0.13

we know lower limit = p-E = 0.27 ..... (1)

Upper limit = p+ E = 0.53 ...... (2)

Substituting E =0.13 IN Equation 1 or 2 , we get p = 0.4

Confidence level = 95%

then Z _{$\dpi{100} \fn_cm \alpha /2$ =} 1.96

We know margin of error E = Z_{$\dpi{100} \fn_cm \alpha /2$}Sqrt (p( 1-p)/n)