Question

assume that a sample is issued, estimate a population porportion p find the 95.5% confidence interval for a sample of size 208 with 31 success. answer as a tri-linear in equality using decimals not % accurate to 3 places.

Answer 1

we have given : n = sample size = 208

x = 31 success .

estimate of a population proportion = phat = x / n = (31 / 208) = 0.149

95.5 % confidence interval for population proportion :

formula : p = (phat ± ( Z critical value * se)

Z critical value =  ± 2 ie -2 to 2 (using table )

se = SQRT ( phat * ( 1-phat) /n)) = SQRT ( 0.149 * (1- 0.149) / 208 ) = SQRT ( 0.00060) = 0.0246

lower limit = phat - Z critical value * se

= 0.149 - ( 2 * 0.0246)

= 0.149 - (0.0492) = 0.099

upper limit = phat + Z critical value * se

= 0.149 + ( 2* 0.0246 )

= 0.198

we can say 95.5 % confident that population proportion is lies within 0.099 to 0.198 .