Below you will find help with selected exercises from the book.

10-6, 10
10-12, 7
10-13, 4
10-15, 8

10-6, 10. Women don't play trombones; leastwise, I never heard of one who did.

The sample represents the target class very poorly (d). In an example like this one it helps to be clear on what the target class is. Technically the speaker might be described as speaking either about women (and claiming that none of them are trombone players) or about trombone players (and claiming that none of them are women). Logically the two claims are the same. In the former case the speaker is generalizing from "women I have heard of" to "all women"; in the latter case from "trombone players I have heard of" to "all trombone players."

Now, the average person who speaks of "all women I know or have heard of" can claim to be starting with a large and fairly random sample. That's just common sense. But because such a small fraction of human beings play the trombone – and really, lots of people who do play the trombone don't talk about it – the large size of the sample class does not help. Any error margin is big enough to miss the trombone players.

But if the sample becomes "trombone players I have known or heard of" then for the average person that becomes a pretty tiny bunch, and likely not representative of all trombone players.

10-12, 7. Is the sample random?

No. Take a moment to recall the definition of a random sample. Every student in Professor Ludlum's courses must be as likely to turn up in the sample as every other student. In one way you might think the evaluation process preserves randomness, given that no one outside the group of students chose a few to submit their opinions. But that's not enough for randomness. Disaffected students, lazy students, and all those satisfied enough with their courses not to bother with evaluations drop out of the sample. They take themselves out, in the sense that no one prevents them from writing evaluations; but actually they are taken out, because the procedure presents an obstacle (it doesn't have to be a great obstacle) to the reports of evaluations by students without strong opinions.

10-13, 4. According to the text, the largest number that he can safely bet hold the belief mentioned is _____ percent.

66. Table 10-1 shows that the error margin for a sample of 250 is ±6. So in 95 percent of all samples, 54–66 percent will hold the belief. Bear in mind that these error margins presuppose a large enough target population—10,000 or larger. In all the questions for 10–13, we have to assume that the student population at George's college is at least that big.

10-15, 8. Overheard: "You're not going to take a course from Harris, are you? I know at least three people who say he's terrible. All three flunked his course, as a matter of fact."

Biased generalization; rather hasty, too. First, note why it is biased. We are not compelled to assume that the three people who call Harris terrible do so because they flunked his course (although that would explain a lot). It's plausible enough to think that they flunked because they considered him a terrible teacher, and so stopped coming to class and doing assignments. The students still form an unrepresentative sample, since we can expect those who fail a course to be in the small minority. As for hastiness, it is naturally possible that the speaker knows plenty of other people who took a course from Harris and didn't call him terrible: Can we leave our minds open about how hastily the speaker reasons? No. That only compounds the bias, since the speaker ignores the evidence against the "Harris is terrible" conclusion.