For Questions 1 and 2, consider the following scenario:

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.

Heidi and Ingrid are sisters, and they bought 30 tickets for the family. When they present 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.

Question 1.

Ingrid is wondering how much, on average, the school is paying out for each ticket.

(a) Find the sample mean value of the tickets.

(b) Find the sample standard deviation.

(c) Construct a 95% confidence interval for the mean value of the tickets.

(d) Does she have a sufficiently-large sample to estimate the mean value of the tickets to within $2 (i.e., give or take $1) at 95% confidence? If not, estimate how large a sample she would need.

(e) Construct a 90% confidence interval for the mean value of the tickets.

(f) Does she have a sufficiently-large sample to estimate the mean value of the tickets to within $2 (i.e., give or take $1) at 90% confidence? If not, estimate how large a sample she would need.

Question 2.

Heidi 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 Heidi's conclusion be at = 0.05? (d) What should Heidi's conclusion be at = 0.01?