In: Statistics and Probability
The manager of a pizza restaurant has recently begun experimenting with a new method of baking pepperoni pizzas. He personally believes that the new method produces a better-tasting pizza, but he would like to base the decision on whether to switch from the old method to the new method on customer reactions. Therefore, he performed an experiment. For 100 randomly selected customers who order a pepperoni pizza for home delivery, he included both an old-style and free new-style pizza in the order. All he asked is that the customers rate the difference between pizzas on a –10 to +10 scale, where –10 means they strongly favor the old style, +10 means they strongly favor the new style, and 0 means they are indifferent between the two styles.
A. what is the business decision to make in this case?
B. once the manager gets the ratings from the customers, how should he make his decision? do you think hypothesis testing is the pest procedure to be used in this business decision making context?
C. if hypothesis testing is used, what will be the null and alternative hypothesis? what does accepting the null hypothesis mean in this case?
D. explain Type 1 and Type 2 errors that the manager may commit when making the decision. what he should do to avoid committing Type 1 error?
(A)
Business decision to make:
Does the new method produce a better tasting pizza?
(B)
Hypothesis testing is the best procedure to be used in this business decision making context. Once the manager gets the ratings from customers, he can apply 2 independent samples t test to check whether there is significant difference in preference between old and new methods. In case as per hypothesis testing, he finds the difference significant, he can adopt the new method.
(C)
H0: Null Hypothesis: (There is no significant difference between the two methods)
HA: Alternative Hypothesis: (There is significant difference between the two methods)
(D)
Type I error:
Reject a true null hypothesis.
Suppose in reality the new method produces better making pizza. But due to hypothesis testing, the manager wrongly concludes that that the new method does not produce better making pizza. Type I error is committed in this situation.
Type II error:
Failure to reject a false null hypothesis.
Suppose in reality the new method does not produce better making pizza. But due to hypothesis testing, the manager wrongly concludes that that the new method produces better making pizza. Type II error is committed in this situation.
To avoid committing Type I Error, the manager should use a lower value for .