To examine the effect of speed of processing training on dementia incidence, community dwelling adults aged 65 years or older without dementia were recruited and randomized to the speed of processing training or no-contact control. Participants randomized to the speed of processing training received computerized, process-based speed of processing training, which involved perceptual practice exercises designed to increase the amount and complexity of information participants could quickly process. Participants completed up to 14 training sessions over a 5-week period. Participants in both the speed training and control groups were then followed for 10 years. Dementia incidence during the 10 years of follow-up among participants in the control group, participants in the speed training group who received 0-10 training sessions, and participants in the speed training group who received 11-14 training sessions is shown below:

Group	Dementia Incidence
Yes	No
Control	97	598
Speed of processing training with 0-10 training sessions	49	355
Speed of processing training with 11-14 training sessions	24	270

a. If dementia incidence is independent of which treatment a participant has received, how many participants in the speed of processing training group with 0-10 training sessions would be expected to have dementia in the 10-year follow-up period?

b. Do participants in the control group, the speed of processing training group who received 0-10 training sessions, and the speed of processing training group who received 11-14 training sessions have different rate of dementia incidence? Perform a hypothesis test using = 0.05.

c. Suppose that the investigator is interested in examining the dose effect of the speed of processing training, i.e., comparing the rate of dementia incidence for participants in the speed of processing training group who received the low dose (0-10 sessions) and high dose (11-14 sessions).

1. Construct a 95% confidence interval for the difference in rate of dementia incidence between participants receiving low dose (0-10 sessions) and high dose (11-14 sessions) training in the speed of processing speed training group.

2. Based on the 95% confidence interval, do you conclude that the dementia incidence rates are different for participants with low dose and high dose training? Justify your answer.

d. Suppose that in the US population, the 10-year dementia incidence rate is 10% for older adults over 65 years. The investigator is interested whether the dementia incidence rate for participants in the control group is the same as the US population. Perform a hypothesis test using = 0.05.