I Sample Size Calculation Calculated by
I. Sample Size Calculation (Calculated by Hand Only)
Example 9.65 Pg. 297
The Chevrolet dealers of a large county are conducting a study to determine the proportion of car owners in the county who are considering the purchase of a new car within the next year. If the population proportion is believed to be no more than 0.15, how many owners must be included in a simple random sample if the dealers want to be 90% confident that the maximum likely error will be no more than 0.02?
Given Data π = 0.15 = 15% z = 1.645 (90%) *Z-Score: 99% = 2.56; 95% = 1.96; 90% = 1.645
E = 0.02
Formula
z² π (1- π) E²
Solution
1.645²0.15 (1- 0.15) 0.02² N = 862.55 => 863 (Always Round Up)
Example 9.63 Pg. 297
A national political candidate has commissioned a study to determine the percentage of registered voters who intend to vote for him in the upcoming election. To have 95% confidence that the sample percentage will be within 3 percentage points of the actual population percentage, how large a simple random sample is required?
Given Data π = 0.5 = 50% *Use 0.5 or 50% when the percentage is not expressed in the problem. z = 1.96 (95%) *Z-Score: 99% = 2.56; 95% = 1.96; 90% = 1.645
E = 0.03
Formula
z² π (1- π) E²
Solution
1.96²0.50 (1- 0.50) 0.03² N = 1067.11 => 1068 (Always Round Up)
Example 9.65 Pg. 297
The Chevrolet dealers of a large county are conducting a study to determine the proportion of car owners in the county who are considering the purchase of a new car within the next year. If the population proportion is believed to be no more than 0.15, how many owners must be included in a simple random sample if the dealers want to be 90% confident that the maximum likely error will be no more than 0.02?
Given Data π = 0.15 = 15% z = 1.645 (90%) *Z-Score: 99% = 2.56; 95% = 1.96; 90% = 1.645
E = 0.02
Formula
z² π (1- π) E²
Solution
1.645²0.15 (1- 0.15) 0.02² N = 862.55 => 863 (Always Round Up)
Example 9.63 Pg. 297
A national political candidate has commissioned a study to determine the percentage of registered voters who intend to vote for him in the upcoming election. To have 95% confidence that the sample percentage will be within 3 percentage points of the actual population percentage, how large a simple random sample is required?
Given Data π = 0.5 = 50% *Use 0.5 or 50% when the percentage is not expressed in the problem. z = 1.96 (95%) *Z-Score: 99% = 2.56; 95% = 1.96; 90% = 1.645
E = 0.03
Formula
z² π (1- π) E²
Solution
1.96²0.50 (1- 0.50) 0.03² N = 1067.11 => 1068 (Always Round Up)