Need a solution with chi-square, not a z test. Thanks
Research has demonstrated that people tend to be attracted to others who are similar to themselves. One study demonstrated that individuals 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 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 Different Initial Initial 19 181 200 Do these date indicate that the number of couples with the same last initial is significantly different that would be expected if couples were matched randomly? Test with a = .05.
Set up hypotheses:
H0: the data follows the expected results
H1: the data does not follow the expected results
Calculate the expected results:
200*0.065 = 13
200 - 13 = 187
So the expected results are 13 and 187.
Now get the chi square test statistic:
= (19-13)^2/13 + (181-187)^2/187
Now, with df = 1 (because there are 2 categories, and df is 1 less than the number of categories), use a table (such as http://www.danielsoper.com/statcalc3/calc.aspx?id=11) to compute the p value.
p = 0.0853
Since this is above the alpha of 0.05, we do not reject H0.
Therefore, there is not enough evidence to conclude that the last initial quantity is different than expected if matched randomly.
Let me know if you have any questions on this, and if you're set, thanks for choosing a high rating.