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

Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Short answer

The given hypothesis test is right-tailed.

Step-by-step solution

Given information

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

Tail of the test

The goodness of fit test is always a right-tailed test.

The chi-square test statistic in a goodness of fit test is as follows:

${\chi }^2=\sum \frac{{\left(O-E\right)}^2}{E}$

Here, if the difference between the observed and the expected frequency is large, the value of the test statistic will shift towards the right side of the curve, and hence, a conclusion can be drawn on whether the null hypothesis should be rejected or not as the observed frequencies do not fit well with the expected frequencies.

Moreover, if the difference between the observed and the expected frequencies is small, it will imply that the given distribution fits well with the expected distribution, and the test statistic value will shift towards the left side of the curve. Thus, the possibility of rejection of the null hypothesis will get diminished on the left tail of the curve.

Therefore, to make a decision about the possible rejection of the null hypothesis, the right tail of the curve is utilized.

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

Thus, the given hypothesis is a right-tailed test.