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

When testing the claim in Exercise 1, what are the observed and expected frequencies for the last digit of 7?

Short answer

The observed frequency for the last digit of 7 is equal to 27.

The expected frequency for the last digit of 7 is equal to 30.

Step-by-step solution

Given information

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

Observed and expected frequencies

The observed frequency corresponding to a particular digit is the same as the frequency tabulated in the question.

Thus, the observed frequency for digit 7 is equal to 27.

The expected frequency corresponding to any digit is computed using the given formula:

\(E = \frac{n}{k}\)

where

n is the sum of all frequencies

k is the number of digits given

The sum of all frequencies is equal to:

\(\begin{aligned}{c}n = 30 + 35 + ......24\\ = 300\end{aligned}\)

The number of digits considered (k) is equal to 10.

Thus, the expected frequency for the last digit of 7 (same for all digits) is computed as follows:

\(\begin{aligned}{c}E = \frac{n}{k}\\ = \frac{{300}}{{10}}\\ = 30\end{aligned}\)

Therefore, the expected frequency for the last digit of 7 is equal to 30.