Give an appropriate response.The tables below show the results of a study examining the incidence of breast cancer among women who exercise regularly and those who do not.The 425 women in the study were split into two age groups, those under 40 and those 40 or older. ?UNDER 40 OVER 40 Breast Cancer Breast CancerRegular exercise Regular exercise For each age group, determine the percentage of women having breast cancer among those exercise regularly and among those who do not exercise regularly. If the two age groups are combined, what

percentage have breast cancer among those who exercise regularly and among those who do not exercise regularly?Explain the apparent inconsistency in these results, and how the design of the study brought about the inconsistency.

What will be an ideal response?

Within each age group, the percentage with breast cancer is lower amongst those who exercise regularly, yet when the age groups are combined, the percentage with breast cancer is higher amongst those who exercise regularly.
Possible answer: The 225 women who do not exercise regularly were unequally divided among the two age groups, 175 in the younger group and 50 in the older group, while the 200 women who do exercise regularly were equally divided into the two age groups. The greater number of younger women, among whom we would expect a lower incidence of breast cancer, virtually guaranteed that the combined rate for the group who do not exercise regularly would be lower.

Mathematics