## Related questions with answers

An insurance company employs agents on a commission basis. It claims that in their first-year agents will earn a mean commission of at least $40,000 and that the population standard deviation is no more than$6,000. A random sample of nine agents found for commission in the first year,

$\sum_{i=1}^9 x_i=333 \text { and } \sum_{i=1}^9\left(x_i-\bar{x}\right)^2=312$

where $x_i$ is measured in thousands of dollars and the population distribution can be assumed to be normal. Test, at the $5 level, the null hypothesis that the population mean is at least$40,000.

Solution

VerifiedFirst, state the null ($H_0$) and alternative ($H_1$) hypotheses of the problem and point out the claim.

$\begin{aligned} &H_0: \mu\geq \$40000 \quad\text{(claim)} \\ & H_1: \mu < \$40000 \end{aligned}$

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