A company claims that 40% of its cereal boxes contain a prize. You buy a random sample of 10 cereal boxes and find that only 2 of the 10 cereal boxes that you bought contain a prize. You wonder if this is evidence that the company is lying or is this a likely result even if the true proportion of cereal boxes with a prize is in fact 40%. You decide to conduct a simulation as follows. Let the numbers 0, 1, 2, 3 represent boxes with a prize. Let the numbers 4, 5, 6, 7, 8, 9 represent boxes without a prize. You generate 25 trials of 10 numbers from the numbers 0 through 9. These trials are below (each column is a trial).

a. Explain why letting the numbers 0, 1, 2, 3 represent boxes with prizes makes sense.

b. Why does each trial have 10 randomly generated numbers in it? What do the 10 numbers represent?

c. Do you think that the results of the simulation provide evidence that the company may be overstating the percent ofcereal boxes that have a prize? Explain.

d. Do you think 25 trials is sufficient? Would it have been better to conduct more trials?

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