Question

a. Here is a proposed sampling strategy to see whether people always wear seatbelts:

Wait outside a supermarket and ask everyone who enters whether they always wear their seatbelts when traveling in a car.

Identify at least ONE source of bias in this proposed strategy. Explain your answer briefly.

b. Here is a proposed design for an experiment to see whether Botox might help severe back pain:

Select 30 people who suffer from severe back pain.  Measure each person’s initial pain level.  Randomly assign 15 of them to be treated with Botox and 15 of them to not be treated.  At the end of 3 weeks, measure each person’s pain level and compare the pain reduction between the groups.

Identify at least ONE thing that would improve this design. Explain your answer briefly.

c. (5 points) Suppose A and B are disjoint events. Are A and B independent events?   

Choose one and explain your answer.

i) Yes

ii) No

iii) It depends.

Answer 1

a)

In this scenario, one source of bias may be response bias. Response bias is the tendency of a person to answer questions on a survey untruthfully. In our setup, this may so happen that when I ask someone whether they always wear their seatbelts when travelling in a car, he or she may lie just to prove himself/herself a responsible person which in reality is false. Here arrives the response bias from that particular person.

b)

In this scenario, in order to improve this design, I must avoid selecting people with widely varying age. That is I must select people with back pain from a group of people whose age doesn't vary much among themselves. This is because older people have more reasons for having back pain which may not be cured with Botox whereas Botox may very quickly cure back pain of a very young person who is much healthy compared to the other. So while selecting I must be very careful with the age of the patient.

c)