Answer to Question #51154 in Statistics and Probability for Mike S.

Question

16.12 Number skills of young men. Suppose that scores on the mathematics part of the National Assessment of Educational Progress (NAEP) test for high school seniors follow a Normal distribution with standard deviation σ = 30. You want to estimate the mean score within ±10 with 90% confidence. How large an SRS of scores must you choose?

16.22 Sampling at the mall. A market researcher chooses at random from women entering a large suburban shopping mall. One outcome of the study is a 95% confidence interval for the mean of “the highest price you would pay for a pair of jeans.”
(a) Explain why this confidence interval does not give useful information about the population of all women
(b) Explain why it may give useful information about the population of women who shop at large suburban malls.

Answer 1

16.12 Number skills of young men. Standard deviation σ = 30. You want to estimate the mean score within ±10 with 90% confidence. An SRS of scores must include at least 2-3 scores.
16.22 One outcome of the study is a 95% confidence interval for the mean of “the highest price you would pay for a pair of jeans.”
(a) This confidence interval does not give useful information about the population of all women, because it just shows the result for the highest price paid, but does not analyze the total population and groups of women.
(b) But it may give useful information about the population of women who shop at large suburban malls, because this confidence interval analyzes prices paid for a pair of jeans, which may be bought at large suburban malls.