Final answer:
The correct use of a chi-square test in hypothesis testing involves assessing whether data fits a specific distribution (goodness-of-fit), examining the independence of two factors (test of independence), or determining if two data sets come from the same distribution (test for homogeneity). Each test is right-tailed and requires expected frequencies to be at least five for valid results.
Step-by-step explanation:
When a chi-square test is used correctly, it serves as a valuable tool in hypothesis testing for assessing different statistical properties in a data set. There are several types of chi-square tests including:
- The goodness-of-fit test which determines if a data set fits a specific distribution, typically used when you suspect that your data follows a known distribution, such as a binomial distribution.
- The test of independence which assesses whether there is an association between two factors or variables in a contingency table.
- The test for homogeneity which compares two data sets to determine if they come from the same distribution.
Each of these tests has some common rules: they are right-tailed tests; each observed and expected cell category must have an expected value of at least five; and the null hypothesis (H0) typically states that there is no effect, or no difference, or that the data follows the assumed distribution.
The chi-square distribution is integral to these tests and how one interprets the probability as the sample size changes. To correctly conduct and interpret these tests, rounding the expected frequency to two decimal places and using a solution sheet (as found in Appendix E) are standard practices.