Question

The claim is that the IQ scores of statistics professors are normally​ distributed, with a mean greater than 133. A sample of 28 professors had a mean IQ score of 138 with a standard deviation of 6. Find the value of the test statistic

Answer 1

Answer:

The value of the test statistic is 4.41

Step-by-step explanation:

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the mean of the sample, $\mu$ is the value of the claim, $\sigma$ is the standard deviation and n is the size of the sample.

In this problem, we have that:

$X = 138, \mu = 133, \sigma = 6, n = 28$

So

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{138 - 133}{\frac{6}{\sqrt{28}}}$

$t = 4.41$

The value of the test statistic is 4.41