For determining the half-lives of radioactive isotopes, it is important to know what the background radiation is for a given detector over a certain period. A γ-ray detection experiment over 300 one-second intervals yielded the following data:

Do these look like observations of a Poisson random variable with mean λ = 3? To answer this question, do the following:
- Find the frequencies of 0, 1, 2, . . . , 8.
- Calculate the sample mean and sample variance. Are they approximately equal to each other?
- Construct a probability histogram with λ = 3 and a relative frequency histogram on the same graph.
- Use α = 0.05 and a chi-square goodness-of-fit test to answer this question.

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