Question

A study investigated whether regular mammograms resulted in fewer deaths from breast cancer over a period of 16 years. Among 30,636 women who never had​ mammograms, 196 died of breast​ cancer, while only166 of 30,223 who had undergone screening died of breast cancer.

​a) Do these results suggest that mammograms may be an effective screening tool to reduce breast cancer​ deaths?

​b) If your conclusion is​ incorrect, which type of error did you​ commit?

Answer 1

Let denote the proportion of people died of breast​ cancer among women who never had​ mammograms and women who had undergone screening died of breast cancer respectively.

Conclusion in problem context :

There is not sufficient evidence to support the claim that mammograms is an effective screening tool to reduce breast cancer​ deaths

b) One may commit a Type II error, i.e. fail to reject H0 when H0 is actually false.