4. Does distance from object affect the eye focus time? Anindustrial engineer is conducting an experiment on eye focus time.She is interested in the effect of the distance of the object fromthe eye on the focus time. Four distances (4’, 6’, 8’, 10’) will bestudied. She has 5 subjects available for the experiment, and hasdecided that she will test each subject at each of the 4 distances;the order in which the distances are tested will be randomlydecided for each study participant. The focus time measurements aregiven in the table below and are posted on in a text fileEyedata.

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(a) What type of experimental design was used in thisexperiment?

(b) What statistical model would you use to analyze thesedata?

(c) What assumptions would be required for the model in (b)?

(d) What evidence do these data provide for / against thehypothesis that the distance has no effect on focus time?

(e) What contrast would you use to test for a difference betweenthe mean focus times for distances of 4’ and 6’? Find a 95%confidence bound for this contrast and interpret.

(f) Test if there is a significant difference between the 4’ and6’ group with the 8’and 10’ group. Clearly state the contrast youwill use, find its unbiased estimator and standard error of theestimator. Next perform the test.

Subject Distance FocusTime

1 4 10

2 4 6

3 4 6

4 4 6

5 4 6

1 6 7

2 6 6

3 6 6

4 6 1

5 6 6

1 8 5

2 8 3

3 8 3

4 8 2

5 8 5

1 10 6

2 10 4

3 10 4

4 10 2

5 10 3