I'm trying to review and I have a question:

If 23 random samples of asbestos fibers found the following samples

31, 29, 19, 18, 31, 28, 34, 27, 34, 30, 16, 18, 26, 27, 27, 18, 24, 22, 28, 24, 21, 17, 24

How should I go about using a Goodness-of-Fit test to show that the Poisson distribution is a plausible model in describing the variability of asbestos fiber counts at the 5% level of significance? Should I set up a table and compute the expected counts versus the observed and proceed from there?

Also, how should I go about giving a point estimate and 95% Confidence Interval estimate of the mean asbestos fiber counts? I am totally lost on this one.

Thank you for any help!