Discuss the below:
Q: A sample of 25 concession stand purchases show a mean purchase of $5.29 with a standard deviation of $3.02. However, a later showing of the same movie, a sample of 25 purchases where the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances.
At α= .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.