Question

Female undergraduates in randomized groups of 14 took part in a self-esteem study. The study measured an index of self-esteem from the point of view of competence, social acceptance, and physical attractiveness. Let x₁, x₂, and x₃ be random variables representing the measure of self-esteem through x₁ (competence), x₂ (social acceptance), and x₃ (attractiveness). Higher index values mean a more positive influence on self-esteem.

Variable	Sample Size	Mean x	Standard Deviation s	Population Mean
x1	14	19.20	3.48	μ1
x2	14	18.71	3.28	μ2
x3	14	17.77	3.53	μ3

(a) Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

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(b) Find a 99% confidence interval for μ₁ − μ₃. (Round your answers to two decimal places.)

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(c) Find a 99% confidence interval for μ₂ − μ₃. (Round your answers to two decimal places.)

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In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 473 eggs in group I boxes, of which a field count showed about 278 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 796 eggs in group II boxes, of which a field count showed about 270 hatched.

(d) Find a 95% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

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Answer 1