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

Given that the P-value for the hypothesis test is 0.501, what do you conclude? Does it appear that the heights were obtained through measurement or that the subjects reported their heights?

Short answer

Since the p-value is greater than 0.05, the null hypothesis is failed to reject.

There is not enough evidence to conclude that the last digits of heights do not occur equally frequently.

Also, it appears that the heights were measured rather than reported because if the heights were reported, the frequencies corresponding to the last digits of 0 and 5 would be significantly greater than the rest of the digits.

Step-by-step solution

Given information

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

Conclusion of the test

The null hypothesis and the alternative hypothesis is written as follows:

\[{H_0}:\]The last digits of the heights of people are equally likely to occur.

\[{H_1}:\]The last digits of the heights of people are not equally likely to occur.

The p-value is equal to 0.501.

The level of significance is equal to 0.05.

Since the p-value is greater than 0.05, the null hypothesis is failed to reject.

Thus, there is not enough evidence to conclude that the last digits of heights do not occur equally frequently.

Reported values vs. measured values

If the heights have been reported, then most of them would have rounded off the values such that a majority of the heights would end in 0 or 5.

Since the frequencies corresponding to the last digits of 0 and 5 are not significantly greater than those of the remaining digits, it can be said that the heights were measured and not reported.