Refer to Exercise 49.
The company that produces the scratchandwin tickets for The FilthyRich Instant Win Super Lottery has assured you that exactly 10% of the tickets are winners (that is, they will pay the purchaser at least a dollar). As an inspector for The FilthyRich Instant Win Super Lottery, Inc., you want to be sure this is precisely the case: too high a percentage of winners would result in excessive payoffs; too few winners might bring on charges of consumer fraud and deception. You select a random sample of 200 tickets from a large order of tickets recently delivered by the ticket supplier and find that 28 of the tickets are winners. Set up a two tailed hypothesis test to determine whether this is sufficient sample evidence to reject the supplier’s claim that, overall, the order contains 10% winners. Use a significance level of 1%.
a. Describe what a Type I error would be in this situation.
b. Describe what a Type II error would be in this situation.
c. Describe the consequences of Type I and Type II error here.