In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50, both averaged 12 years of schooling completed, with an SD of 3 years. a) Predict the educational level of a woman whose husband has completed 18 years of schooling b) Predict the educational level of a man whose wife has completed 15 years of schooling. c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible?

Question
In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50, both averaged 12 years of schooling completed, with an SD of 3 years.
a) Predict the educational level of a woman whose husband has completed 18 years of schooling b) Predict the educational level of a man whose wife has completed 15 years of schooling. c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible?

Answers (1)

2021-02-01
a) The educational level of women whose husband has completed 18 years of schooling:
18 is average +2SD
18 = 12 + 6 = 12 + 2SD
now multiply the correlation coefficient (0.5) by 2: 0.5 * 2 = 1
then multiply 1 by SD of 3: 1 * SD = 1 * 3 = 3
now add 3 to 12: 12 + 3 = 15
15 is the educational level of a women
b) The educational level of man whose wife has completed 15 years of schooling:
15 is average +1SD
15 = 12 + 3 = 15 + 1SD
now multiply the correlation coefficient (0.5) by 1: 0.5 * 1 = 0.5
then multiply 0.5 by SD of 3: 0.5 * SD = 0.5 * 3 = 1.5
now add 1.5 to 12: 12 + 1.5 = 13.5
13.5 is the educational level of a men
c) If all the data were aviable, we colud see in the scatter diagram that. the variation around the least squre lines is very high, that giving this conflcting results.
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