Using Data to Investigate Questions and Solve Problems

Candy Corn and Profit

Candy Corn and Packaging

During Halloween season, many consumers like to purchase and enjoy candy corn and candy pumpkins. A certain company just purchased a new machine that seals the packages of these tasty treats. This machine can seal a larger number of bags per hour and can save the company a significant amount of money which will add to the profit margin. A statistician was hired to check to make sure that the new machine is working effectively by sealing packages that require a force of 4.5 Newtons (N) and, and the force should be within 8% of the target.


  1. The 100 bags were randomly selected and were representative of the population.

  2. The data for Force were approximately symmetric with no outliers, but with a sample size n=100 which is larger than 20, it is safe to conduct a one-sample equivalence test.

  1. Each randomly selected package was independent of others.

  2. The target power of .8 was met.


The following tables and graph list the relevant statistics for a one-sample equivalence test:

We can look at a couple of values to draw the same conclusion.

  1. When looking at Table 1 and the graph, it is clear that the confidence interval is contained within the equivalence interval. Hence, we conclude the alternative hypothesis which is equivalence.

  2. When looking at Table 2, it is clear that the p-values for both differences is less than .05. Hence,

  3. we can conclude the alternative hypothesis which is equivalence.


It appears that the new packaging machine is sealing the bags of candy corn to the desired target. Thus, the company should consider buying more machines to make production less expensive and more efficient.