Final answer:
The statement is True; in a goodness-of-fit test, the larger the difference between observed and expected values, the larger the test statistic, which falls in the right tail of the chi-square distribution, indicating a potential rejection of the null hypothesis.
Step-by-step explanation:
The statement, 'In general, if the observed values and expected values of a goodness-of-fit test are not close together, then the test statistic can get very large and on a graph will be way out in the right tail,' is True. A goodness-of-fit test uses the chi-square distribution to compare the observed values to the expected values if the null hypothesis is true. If there's a large difference between observed and expected values, the resulting chi-square test statistic will be large, indicating a higher likelihood of rejecting the null hypothesis. This is because the test is almost always right-tailed, which means that larger test statistics fall into the right tail of the chi-square distribution curve.
In the scenario where the expected and observed values diverge significantly, the test statistic increases, reflecting the low probability (small p-value) that the observed differences are due to random chance alone. The number of degrees of freedom for this test is 'number of categories - 1', and it's important to note that each expected value should be at least five to properly conduct the test.