Question

A statistician wishes to test the claim that the standard deviation of the weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 20 firemen and found s = 27.2 pounds.

Assuming that the weights of firemen are normally distributed, to test her research hypothesis the statistician would use a chi-square test. In that case, what is the computed test value?

Answer 1

Answer on Question#36994 – Math – Statistics and Probability

A statistician wishes to test the claim that the standard deviation of the weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 20 firemen and found $s = 27.2$ pounds.

Assuming that the weights of firemen are normally distributed, to test her research hypothesis the statistician would use a chi-square test. In that case, what is the computed test value?

Solution

Let’s calculate the chi square statistic:

$$\chi^2 = \frac{(O - E)^2}{E},$$

where $O$ – observed standard deviation, $E$ – expected standard deviation.

So

$$\chi^2 = \frac{(27.2 - 25)^2}{25} = 0.1936.$$

Our degrees of freedom $(df)$ are sample sizes minus 1:

$$df = 20 - 1 = 19.$$

Then we use Chi Square distribution table.

Checking the table of critical values of the chi-square distribution for 19 degrees of freedom, we find that $p = 1.0$.

Answer: 1.0.