# Question: The exponential probability distribution can be used to model waiting

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?

(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?

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