One of the problems with a study such as this one is the small size of the samples. If you wanted to
estimate the proportion of a certain color of candy to within 2% of the actual proportion, how many
individual pieces of candy must you sample? Assume you want to be 90% confident in your results and
no previous information is known regarding the proportion values. Based on the total count of candies in
your package, approximately how many packages of candy would be required to obtain this minimum sample size?
To estimate the proportion of a certain color of candy with a specified level of confidence and margin of error, you can use the formula for sample size calculation.
The formula for sample size calculation to estimate a proportion is:
n = (Z^2 * p * (1-p))/(E^2)
Where:
- n is the desired sample size
- Z is the Z-score corresponding to the desired level of confidence (90% confidence corresponds to a Z-score of 1.645)
- p is the estimated proportion of the certain color of candy (this is unknown, so we'll assume it to be 0.5 to be conservative)
- E is the margin of error (in this case, 2% of the estimated proportion, so 0.02)
Let's plug in the values into the formula:
n = (1.645^2 * 0.5 * (1-0.5))/(0.02^2)
n ≈ 422.83
Since you cannot have a fractional sample size, you would need to round up to the nearest whole number. Therefore, you would need to sample at least 423 individual pieces of candy to estimate the proportion of the certain color of candy.
To estimate the number of candy packages needed, you would need to know the total count of candies in each package. Let's say each package contains X number of candies.
The approximate number of packages required would be:
Number of packages = n / X
For example, if each package contains 20 candies:
Number of packages ≈ 423 / 20
Number of packages ≈ 21.15
Again, you cannot have a fractional number of packages, so you would need to round up to the nearest whole number. Therefore, approximately 22 packages of candy would be required to obtain the minimum sample size of 423 individual pieces of candy.