Exercise 9.5 describes two surveys conducted in the United Kingdom: one in 1999 and one in 2004.
a. A 95% confidence interval for the population proportion who judge a book by its cover would be (0.63, 0.69) based on a sample of 1,000 people in the first survey, and (0.05, 0.09) based on a sample of 1,000 people in the second survey. Which survey suggests that a majority of people judge a book by its cover: the first, the second, both, or neither?
b. If the surveys had each used 2,000 people instead of 1,000, would the confidence intervals be narrower or wider?
c. Suppose the surveyors decided in advance that they wanted a margin of error no more than m 0.04. What sample size should be used?
Exercise 5
A survey conducted in the United Kingdom in 1999 showed that "66% of people said they chose books on the basis of their jackets, and nearly 75% said they were influenced by book reviews."9 A survey conducted in 2004 showed that "one in four of those polled said the last book they read was on the basis of what a colleague or family member had told them [. . .] Only oyalty to a favoured author counted as much, with 26% of readers saying their last choice of a book for pleasure was because they had read others by the same author. In a disappointing result for the promotional teams who spend up to 100 million pounds on book advertising every year, only 6% said they chose a book because they saw it advertised, with 7% citing the cover design as the deciding factor."10
a. Which survey apparently allowed for overlapping categories: the one from 1999 or the one from 2004, or both, or neither?
b. Based on the first survey, what is your best guess for the proportion of all people who choose books on the basis of their jackets?
c. The percentage of people who "judge a book by its cover" seems to be 66% according to the first survey, and only 7% according to the second one. What is the best explanation for these percentages being so different?
d. Suppose about 1,000 people had been sampled for the second survey, and a 95% confidence interval for population proportion who judge a book by its cover was found to be (0.05, 0.09). Which one of these is the best interpretation of this interval?
1. We have produced an interval with a 95% probability of containing the proportion of all people for whom a book's cover was the deciding factor in choosing the last book they read.
2. We have produced an interval with a 95% probability of containing the proportion of all people for whom a book's cover was among the deciding factors in choosing the last book they read.
3. We have produced an interval with a 95% probability of containing the sample proportion of people for whom a book's cover was the deciding factor in choosing the last book they read.
4. We have produced an interval with a 95% probability of containing the sample proportion of people for whom a book's cover was among the deciding factors in choosing the last book they read.