Question

At a confidence level of 95% a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the sample size had been larger and the estimate of the population proportion the same, this 95% confidence interval estimate as compared to the first interval estimate would be

Answer 1

Solution :

given that

Lower confidence interval = 0.68

Upper confidence interval = 0.75

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

=   = (0.65+0.75) / 2

Point estimate = =0.7

Margin of error = E = Upper confidence interval -

=0.75-0.7

Margin of error = E = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.96 / 0.05)² * 0.0.7 * 1-0.7

= 323

Sample size = 323