In a study on the fertility of married women conducted by Martin O’Connell and Carolyn C. Rogers for the Census Bureau in 1979, two groups of childless wives aged 25 to 29 were selected at random, and each was asked if she eventually planned to have a child. One group was selected from among wives married less than two years and the other from among wives married five years. Suppose that 240 of the 300 wives married less than two years planned to have children some day compared to 288 of the 400 wives married five years. Can we conclude that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years? Make use of a P -value.

Answer:we cannot conclude hat the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five yearsStep-by-step explanation:Given that in a study on the fertility of married women conducted by Martin O’Connell and Carolyn C. Rogers for the Census Bureau in 1979, two groups of childless wives aged 25 to 29 were selected at random, and each was asked if she eventually planned to have a child. One group was selected from among wives married less than two years and the other from among wives married five years.Let X be the group married less than 2 years and Y less than 5 years                          X        Y     TotalSample size   300   300    600Favouring       240   288    528p                      0.8     0.96  0.88[tex]H_0: p_x=p_y\\H_a: p_x>p_y[/tex]p difference = -0.16Std error for difference = [tex]\sqrt{0.88*0.12/600} =0.01327[/tex]Test statistic = p difference/std error=-6.03p value <0.000001Since p is less than alpha 0.05 we cannot conclude hat the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years