Question

A senator wishes to estimate the proportion of United States voters who favor abolishing the Electoral College.How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 3%?

Answer 1

SOLUTION:

From given data,

How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 3%

Sample Size for 98% CI ,

Margin of Error = E = 3% = 3/100 = 0.03 without

98% confidence interval

Confidence interval is 98%

98% = 98/100 = 0.98

= 1 - Confidence interval = 1-0.98 = 0.02

/2 = 0.02 / 2

= 0.01

Z_/2 = Z_0.01  = 2.33 (closest value from z table)

The formula for the sample size in the case of single proportion is

=   ( 1 - ) (Z_/2 / E )²

Since we don't have preliminary estimate, we use the sample proportion, = 0.5, which requires the maximum n

=  0.5 ( 1 - 0.5) (2.33/ 0.03)²

= 6786.125

= 6786