Final answer:
The expected frequency for each side of the die when rolled 120 times is 20. A goodness-of-fit test is used to assess the fairness of the die, and the hypothesis is rejected if the p-value is less than the significance level.
Step-by-step explanation:
To answer the student's question regarding the expected frequency when a six-sided die is rolled 120 times, we start by assuming that if the die is fair, each of the six sides should come up an equal number of times. Therefore, the expected frequency for each number (1 through 6) is 120 rolls divided by 6 sides, resulting in an expected frequency of 20 for each number.
The type of test used to determine if the die is fair is a goodness-of-fit test. To conduct this test, one would calculate the observed frequencies from the data in Table 11.34, then compare these observed frequencies with the expected frequencies using the chi-square statistic. If the resulting p-value from the chi-square test is low (typically less than 0.05), this suggests that the observed data are significantly different from what we would expect if the die were fair, and thus we would reject the null hypothesis that the die is fair.
While the question provides some guidance suggesting that if the p-value is 0.0113, in general, we do not reject the null hypothesis, it's critical to compare the p-value with the significance level chosen for the hypothesis test. If the p-value is less than or equal to the significance level, then we reject the null hypothesis and conclude that the die may not be fair. Conversely, if the p-value is greater than the significance level, we do not reject the null hypothesis.