Final answer:
The question is about conducting a chi-square Goodness-of-Fit test to determine if a die is fair. It involves comparing a test statistic to a critical value at a 1% significance level to decide whether to accept or reject the null hypothesis of a uniform distribution.
Step-by-step explanation:
The question involves using a chi-square Goodness-of-Fit hypothesis test to determine whether a six-sided die is fair, based on the results of 96 rolls. For a fair die, the expected frequency for each outcome (1 through 6) would be equally distributed; therefore, each number should appear approximately 16 times (96 rolls divided by 6 possible outcomes). To conduct the test, we state the null hypothesis (H0): The die has the uniform distribution, against the alternative hypothesis (Ha): The die does not have the uniform distribution. The critical value is used to determine if the observed frequencies are significantly different from the expected frequencies.
The test statistic is compared against a critical value from the chi-square distribution table corresponding to the degrees of freedom, calculated as the number of categories minus one (5 in this case, since a six-sided die has 6 possible outcomes) and the chosen level of significance. In this scenario, the significance level is 1%, and you would select the appropriate critical value to compare your test statistic to. If the test statistic exceeds the critical value, the null hypothesis is rejected, indicating that the die may not be fair.