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When an environmental company went out to measure the radon level at a house it found that the radon exceeded the standard level. The environmental company decided to measure the average amount of radon detected by randomly checking the house’s water supply twenty times over the next two months.

The graphical display of the data was approximately normal. The environmental company ran a test to see if there was evidence the average amount of radon in this house was significantly higher than it should be.

Why should the company run a $t$-test rather than a $z$-test?

A

The company is using the sample standard deviation to estimate the population standard deviation.

B

The company is using the sample mean rather than the population mean.

C

$Z$ distributions can only be used in means when $n > 30$.

D

$Z$ distributions can only be used when the population is exactly normal.

E

$Z$ distributions can only be used in inferencing for proportions.

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