Question

Exercises 1–5 refer to the sample data in the following table, which summarizes the last digits of the heights (cm) of 300 randomly selected subjects (from Data Set 1 “Body Data” in Appendix B). Assume that we want to use a 0.05 significance level to test the claim that the data are from a population having the property that the last digits are all equally likely.

Last Digit	0	1	2	3	4	5	6	7	8	9
Frequency	30	35	24	25	35	36	37	27	27	24

If using a 0.05 significance level to test the stated claim, find the number of degrees of freedom.

Short answer

The degrees of freedom for the given test are equal to 9.

Step-by-step solution

Given information

The last digits of the heights of a sample of people are tabulated along with their respective frequencies.

Degrees of freedom

The degrees of freedom for the goodness of fit test has the following formula:

\(df = k - 1\)

Where k is the number of categories.

Here, the hypothesis test to test the claim that the given digits occur equally frequently is a goodness of fit test.

k denotes the number of last digits equal to 10.

The degrees of freedom are computed as shown:

\(\begin{aligned}{c}df = k - 1\\ = 10 - 1\\ = 9\end{aligned}\)

Thus, the degrees of freedom for the given test are equal to 9.