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).