D.15 Answers: Making decisions

Answers to exercises in Sect. 15.8.

Answer to Exercise 15.1: 1. Yes! Seems likely there is a problem (we can’t be certain). 2. Assuming the die was fair, I would not expect to get a 6 ten times in a row; sounds highly unusual.
Answer to Exercise 15.2: 1. That the population mean is 12 inches, as claimed. We have no evidence to refute this claim. 2. First: the population mean diameter is \(\mu=12\) inches; the sample mean is not 12 inches due to sampling variation. Second: the population mean diamter isn’t 12 inches, reflected in the sample. 3. 11.48 is 0.52 inches from the target of 12; seems unlikely that the sample mean would be that far from 12 inches through sampling variation alone. 4. \(\bar{x} = 11.25\) inches isfurther from \(\mu=12\) that \(\bar{x} = 11.48\): claim probably not supported. 5. Smaller sample sizes: sample mean would vary more (in general, larger samples give more precise estimates).