50 components are placed on a life test. The recorded times to failure, in hours, are given in the Excel file "Assignment 3 Question 2 Data.xls". The sample data are suspected of coming from a population of lifetimes that can be adequately modeled by an exponential distribution. Analyze the sample data in the following steps: (a) Construct a histogram using cell intervals of size 500 hrs in the range of 0 to 5000 hrs. (b) What type of data is it? Estimate failure rate and the MTTF using the appropriate formula for the type of data you identified. Hint: Identify the type of data among those types mentioned in slide 21, Lecture 6, and choose the appropriate estimating formula. (c) Estimate the median time to failure using the estimate of from Question 2(b). Hint: Use CDF. (d) Test the adequateness of the exponential model using the chi-square goodness of fit test and a confidence (or significance) level of 90%. Use the same intervals as in Question 2(a), combining everything greater than 2000 hr into one group. What is your conclusion? (e) Calculate the 80% and 95% 2-sided confidence bounds for . Hint: A complete data sample is equivalent to the test having been planned to stop when all units fail, i.e. number of failures = sample size. (f) Suppose the test had been planned to stop upon the 5th failure, and hence ended at 112 hr. What is the type of data? Estimate , MTTF, and a 60% two-sided confidence interval using the appropriate formula. (g) Repeat Question 2(f) supposing the test had been planned to stop at 150 hr. What is the type of data? Estimate , MTTF, and a 60% two-sided confidence interval using the appropriate formula.