According to recent research (www.nas.org) married couples who met their spouse through an online dating service may have a different divorce rate than those who met €œoff-line.€ (Online Mating From Proceedings of the National Academy of Sciences of the United States of America. Copyright (c) 2008 National Academy of Sciences. Reproduced by the permission of National Academy of Sciences.) The survey polled couples who married between 2005 and 2012. The baseline divorce rate (by 2013) for off-line marriages in this cohort is 7.73%. The report gives the following divorce statistics according to the on-line dating service where the couple met:

a) If the divorce rate were the same for these couples as for those who met offline, how many divorces would you expect for each group of couples?
b) To test whether these couples are different from offline couples, will you perform a goodness-of-fit test, a test of homogeneity, or a test of independence?
c) State the hypotheses.
d) Check the conditions.
e) Find the standardized residuals and the chi-square components.
f) State the number of degrees of freedom and find x2 and the P-value.
g) State your conclusion.
h) Online dating services are a billion-dollar business in the U.S. Does it change your conclusion to know that the study was funded by eHarmony?

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Couples (n) Divorces/Separations Service eHarmony Match Plenty of Fish Yahoo Small Sites 791 775 201 227 29 58 20 12 37