Question

Suppose you observe a sample data set consisting of n=64 inter-arrival times X1,…,X64 for the subway, measured in minutes. As before, we assume the statistical model that X1,…,X64∼iidexp(λ) for some unknown parameter λ>0. In this data set, you observe that the sample mean is 164∑64i=1Xi=7.8.

Additional Instructions: For best results, please adhere to the following guidelines and reminders:

For the upcoming calculations, please truncate qα/2 at 2 decimal places, instead of a more exact value. For example, if qα/2=3.84941, use 3.84 instead of 3.85 or 3.849.

Input answers truncated at 4 decimal places. For example, if your calculations yield 11.327458, use 11.3274 instead of 11.3275 or 11.32745.

You will be computing CIs at asymptotic level 90%.

Using the ‘solve method' (refer to the slide ‘Three solutions'), construct a confidence interval Isolve with asymptotic level 90% for the unknown parameter λ.

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Using the ‘plug-in method' Iplug−in (refer to the slide ‘Three solutions'), construct a confidence interval with asymptotic level 90% for the unknown parameter λ.

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Which interval is narrower?


Isolve
Iplug−in
unanswered
Which of these confidence intervals is centered about the sample estimate, λ^n?


Isolve
Iplug−in
Both
Neither

Answer 1

We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.

Answer 2

I plugin
I plugin