Question

1. A hypothesis has been proposed that breast cancer in women is caused in part by events that occur between the age of menarche (time of 1st menstruation) and the age of first childbirth. The hypothesis is that the risk for breast cancer increases as the length of this time interval increases. To test this hypothesis an international study was set up. Breast cancer cases were identified among women in selected hospitals in the United States, Greece, Yugoslavia, Brazil, Taiwan and Japan. Controls were chosen from women of comparable age who were in the hospitals at the same time as the cases but did not have breast cancer. The women with at least 1 birth were divided in to two categories 1) women whose age at first birth <=29; 2) women whose age at first birth >=30. The following results were found: among women with at least 1 birth: 683 out of 3220 (21.2%) women with breast cancer and 1498 out of 10,245 (14.6%) women without breast cancer had an age at first birth >=30. a. Fill in the following 2x2 table Breast Cancer cases Controls age at first birth <=29 age at first birth >=30 Total b. Conduct the appropriate hypothesis test and assess whether this difference is significant or simply due to chance. Suppose we are willing to commit a Type I error (falsely rejecting the null hypothesis 5% of the time). Be sure to state the null and alternative statistical hypothesis, compute the test statistic, calculate the p-value and make the decision. c. Use SAS to confirm your p-value and that the test statistic you computed once squared compares to the Chi-square test statistic on the SAS output.

Answer 1

a)

b)