The exponential probability distribution can be used to model waiting time in line or the lifetime of electronic components. Its density function is skewed right. Suppose the wait-time in a line can be modeled by the exponential distribution with µ = σ = 5 minutes.
(a) Simulate obtaining 100 simple random samples of size n = 10 from the population described. That is, simulate obtaining a simple random sample of 10 individuals waiting in a line where the wait time is expected to be 5 minutes.
(b) Test the null hypothesis H0: µ = 5 versus the alternative H1: µ ≠ 5 for each of the 100 simulated simple random samples.
(c) If we test this hypothesis at the α = 0.05 level of significance, how many of the 100 samples would you expect to result in a Type I error?
(d) Count the number of samples that lead to a rejection of the null hypothesis. Is it close to the expected value determined in part (c)? What might account for any discrepancies?

  • CreatedApril 28, 2015
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