z statistic for 36 salespeople averaging 17 deals

Question

A manager believes his team closes at most $15$ deals per person per week on average. He samples $36$ salespeople in one week and finds a sample mean of $17$ deals and a sample variance of $9$ . He tests whether the true mean exceeds $15$ . Assuming random sampling and roughly normal counts, what is the value of his test statistic?

Short answer

$4$ . With $n=36$ a z statistic is appropriate: $z=\dfrac{17-15}{3/\sqrt{36}}=\dfrac{2}{0.5}=4$ .

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Lessons behind this question

Maximum Likelihood Estimation: Score and Log-Likelihood
Covariance and Correlation
The Hypothesis Testing Framework

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