In a study of the effects of smoking cigarettes during pregnancy, researchers examined the placenta from each of 58 women after childbirth. They noted the presence or absence (P or A) of a particular placental abnormality -atrophied villi. In addition, each woman was categorized as a non-smoker (N), moderate smoker (M), or heavy smoker (H).The following table shows, for each woman, an ID number (#) and the results for smoking (S) and atrophied villi (V).

(a) Test for a relationship between smoking status and atrophied villi. Use a chi-square test at α = 0.05.
(b) Prepare a table that shows the total number of women in each smoking category, and the number and percentage in each category who had atrophied villi.
(c) What pattern appears in the table of part (b) that is not used by the test of part (a)?

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PPAPAPAPAPPP HHHNNMMHHMHH 789012345678 #|4 4 4 4 5 5 5 5 5 5.3 5 AAAAPAPPAAAAA P MNNNHNHHNMNHM M 2345, 6 7 8 9 0 1 2 3 4 3333333344444 # 3 4 PAPPAAPAPAAPA A HNMNMHMNNNNMN N 7, 8 9 0 1 2 3 4 6789 0 # 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 A A A P P A A P A P P A P MNMMMHNNMNNHM M # 12345, 6 7 8 9 0 1 2 3 4 5