WK 3 Assignment
BUS 461
Problem 8-33. You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 2% of the actual value?
Our main goal for this assignment is to carefully choose the sample size that will allow the examiner to build a case whether people have a preference between Coke or Pepsi. We know that a sample is “a subset of the population, often randomly chosen and preferably representative of the population as a whole. Sample size is designed to produce a recommended level accuracy,” (Albright & Winston, 2017).
| Sample Size for Variance of Proportions | |
| Confidence Level | 95% |
| Half-Length Interval | .02 |
| Sample Size (A) | 0.5000 |
| Sample Size (B) | 0.5000 |
| Test Sample Size | 4802 |
Using the formula for estimating the difference between proportions, we can conclude that based on the results of the formula, 4802 selected personnel are required for testing. :
Sample size: n
Coke: a = 0.5
Pepsi: b = 0.5
Half Length Interval: 0.02
n = (z-multiple/b) ^2 [a (1-a) + b (1-b)]
n = (98)^2 [0.5 (1-0.5) + 0.5 (1-0.5)]
n = (98)^2 (.25+.25)
n = 9604 x 0.5
n = 4802
Reference:
Albright, S. C, & Winston, W. L. (2017). Business analytics: Data analysis and decision making (6th ed.). Retrieved from https://redshelf.com/