Statistics | Confidence Intervals

1. Beth’s Butter Works has test marketed their new low-fat butter substitute with two different styles of packaging. They are trying to estimate the sales of the product for each type of packaging. Average daily sales of the product in the traditional plastic tub was 100 units across 16 stores, and sales of the product in gold foil wrap had the same average sales of 100 units across a sample of 25 stores. The standard deviation for each of the samples is 20.

Management at Beth’s would like to know with a 95% confidence how many units they can expect to sell per store. 

2. The marketing team at Beth’s Butter Works decided they preferred the traditional plastic tub packaging, but they wanted a more refined estimate of potential sales. They launched a third test at a regional level across 100 stores. These 100 stores had average daily sales of 140 units with a standard deviation of 50.

Calculate the 99%, 95%, and 68% confidence intervals for the average number of units Beth’s Butter Works can anticipate to sell.