Question

A poll was conducted to find out the percentage of people who will support a state bill in Massachusetts. How large the sample size n need to be polled to make sure the 95% confidence interval has a margin of error of at most 2.6%.

Answer 1

Solution :

Given that,

= 0.5 ( use=0.5 }

1 - = 1 - 0.5 = 0.5

margin of error = E = 2.6% = 0.026

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= (1.96 / 0.026)2 * 0.5 * 0.5

= 1420.71

Sample size =1421