15.8 Exercises

Selected answers are available in Sect. D.15.

Exercise 15.1 Suppose you are playing a die-based game, and your opponent rolls a 6 ten times in a row.

1. Do you think there is a problem with the die?
2. Explain how you came to this decision.

Exercise 15.2 In a 2012 advertisement, an Australian pizza company claimed that their 12-inch pizzas were ‘real 12-inch pizzas,’ unlike another brand (Dunn 2012).

1. What is a reasonable assumption to make to test this claim?
2. The claim is based on a sample of 125 pizzas, for which the sample mean pizza diameter was \(\bar{x} = 11.48\) inches. What are the two reasons why the sample mean is not 12-inches?
3. Does the claim appear to be supported by, or contradicted by, the data? Why?
4. Would your conclusion change if the sample mean was \(\bar{x} = 11.25\) inches, rather than 11.48 inches? Does the claim appear to be supported by, or contradicted by, the data? Why?
5. Does your answer depend on the sample size? For example, is observing a sample mean of 11.25 inches from a sample of size 10 equivalent to observing a sample mean of 11.25 inches from a sample of size 125?