In an article, authors survey Black Friday shoppers. One question was "How many hours do you usually spend shopping on Black Friday?"
1. How many Black Friday shoppers should be included in a sample designed to estimate the average number of hours spent shopping on Black Friday if you want the estimate to deviate no more than 0.5 hour from the true mean?
2. Devise a sampling plan for collecting the data that will likely result in a representative sample.
The number of shoppers to be included in a sample will be determined by the population at hand and the kind of deviation expected from the mean. in our case, the mean deviation is 0.5. To get the number of shoppers expected, it will be 0.5* 24 hrs in back Friday = 12 shoppers.
The best sampling plan in this case will be simple random sampling without replacement where you will select the 12 shoppers randomly from the entire population of the shoppers. assuming we have 120 shoppers, you divide them into 10 groups and then choose two shoppers from each group without replacement. you will get a sample of 12 shoppers to work with.