An obstetrician wants to learn whether the amount of prenatal care and the wantedness of the pregnancy are associated. He randomly selects 939 women who had recently given birth and asks them to disclose whether their pregnancy was intended, unintended or mistimed. In addition they were to disclose when they started receiving prenatal care. If ever. The results of the survey are as follows

Wantedness of pregnancy Less than 3 months 3 to 5 months More than 5 months
intended 593 26 33
unintended 64 8 11
mistimed 169 19 16

a. compute the expected values of each cell under the assumption of independence
b. verify that the requirements for performing a chi square test of independence are satisfied.
c. Compute the chi square test statistic
d. Test whether prenatal care and the wantedness of pregnancy are independed at the α=0.05 level of significance

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