A school has been selling raffle tickets to raise funds for the school library. Each ticket is sold for $5, and the school has sold many such tickets. Each ticket has a code. When a ticket is presented at the library book sale, it can be redeemed for $1, $5, or $10. The dollar amount being assigned to each ticket is determined by a lottery before the book sale. Rachael has bought 30 tickets for her family. When she presents these 30 tickets at the book sale,
• 14 tickets are redeemed for $1,
• 12 tickets are redeemed for $5, and• 4 tickets are redeemed for $10.
She is wondering whether the school is actually losing money out of the raffle.
(a) Formulate the null and alternative hypotheses that can be used to determine whether the school is losing money out of the raffle. Note that the issue is whether the school is losing money, not whether the school is breaking even. Please think about what the implication is when formulating the null and alternative hypotheses.
(b) Find the p-value for the hypothesis test.
(c) What should Rachael’s conclusion be at α = 0.05?
(d) What should Rachael’s conclusion be at α = 0.01?