Question

10.3 #8

Isabel Myers was a pioneer in the study of personality types. She identified four basic personality preferences that are described at length in the book Manual: A Guide to the Development and Use of the Myers-Briggs Type Indicator, by Myers and McCaulley.† Marriage counselors know that couples who have none of the four preferences in common may have a stormy marriage. A random sample of 375 married couples found that 287 had two or more personality preferences in common. In another random sample of 571 married couples, it was found that only 27 had no preferences in common. Let p₁ be the population proportion of all married couples who have two or more personality preferences in common. Let p₂ be the population proportion of all married couples who have no personality preferences in common.

(a) Find a 99% confidence interval for p₁ – p₂. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

= 287/375 = 0.765

= 27/571 = 0.047

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                     = (0.765 * 375 + 0.047 * 571)/(375 + 571)

                                                     = 0.332

At 99% confidence interval the critical value is z_0.005 = 2.58

The 99% confidence interval for P1 - P2 is

() +/- z_0.005 * sqrt(P * (1 - P) * (1/n1 + 1/n2))

= (0.765 - 0.047) +/- 2.58 * sqrt(0.332 * (1 - 0.332) * (1/375 + 1/571))

= 0.718 +/- 0.081

= 0.637, 0.799