In: Statistics and Probability
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%?
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 = Z0.01 = 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