Research has demonstrated that people tend to be attracted to others who are similar to themselves. One study demonstrated that indiciduals are disproportionately more likely to marry those with surnames that begin with the same last letter as their own (Jones, Pelham, Carvallo, & Mirenberg, 2004). The researchers began by looking at marriage records and recording the surname for each groom and the maiden name of each bride. From these records it is possible to calculate the probability of randomly matching a bride and a groom whose last names begin with the same letter. Suppose that this probability is only 6.5%. Next, a sample of n=200 married couples is selected and the number who shared the same last initial at the time they were married is counted. The resulting observed frequencies are as follows:
Same Initial Different Initials 200
19 181
Do these data indicate that the number of couples with the same last initial is significantly different than would be expected if couples were matched randomly? Test with α = .05.
The expected proportion for the same initials is 0.065 and for different initials it is 0.935. Multiply these (one at time) with 200 to get the expected frequencies. Apply the chi-square formula and then obtain the tabulated chi square and make your conclusion.