A quality control engineer studied the relationship between years of experience as a system control engineer and the capacity of the engineer to complete within a given time a complex control design including the debugging of all computer programs and control devices. A group of 25 engineers having widely differing amounts of experience (measured in months of experience) was given the same control design project. The results of the study are given in the following table with y = 1 if the project was successfully completed in the allocated time and y = 0 if the project was not successfully completed.

a. Determine whether experience is associated with the probability of completing the task.
b. Compute the probability of successfully completing the task for an engineer having 24 months of experience. Place a 95% confidence interval on your estimate.

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Months of Months of Experience Project SuccessExperienceProject Success 17 24 27 10 10 31 12 13