The gestation period of gray squirrels in captivity is listed as 44 days. It is recognized that the potential life span of animals is rarely attained in nature, but the gestation period could be either shorter or longer. Suppose the gestation period of a sample of 81 squirrels living in the wild is measured and the mean length of gestation time is 42.5 days. Test the hypothesis that squirrels living in the wild have the same gestation period as those in captivity at the 0.05 level of significance. Assume that σ = 5 days. Use the four step process for Hypothesis Testing.
Step 1 - State Hypothesis in context of the problem.
Step 2 - Gather data, check assumptions, and find rejection region using α.
Step 3 - Calculate the appropriate test statistic and p-value.
Step 4 - State conclusion in context of the problem.