Final answer:
To conduct a hypothesis test, use a chi-square goodness-of-fit test to determine if the outcomes of the rolled die are equally likely. Calculate the expected frequencies, chi-square test statistic, critical value, and compare the results to determine the conclusion.
Step-by-step explanation:
To conduct a hypothesis test to determine if the outcomes of the rolled die are equally likely, we can use a chi-square goodness-of-fit test. The null hypothesis (H0) is that the outcomes are equally likely, and the alternative hypothesis (Ha) is that the outcomes are not equally likely. We will use a significance level of 0.10.
1. Calculate the expected frequencies for each outcome by dividing the total number of rolls (≥200) by the number of possible outcomes (6). This gives us an expected frequency of approximately 33.33 for each outcome.
2. Calculate the chi-square test statistic by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies: Χ² = Σ((Observed - Expected)² / Expected).
3. Determine the critical value for the chi-square test at a significance level of 0.10 and degrees of freedom equal to the number of outcomes minus 1 (6 - 1 = 5). Look up the chi-square critical value for 5 degrees of freedom in a chi-square distribution table.
4. Compare the test statistic to the critical value. If the test statistic is greater than the critical value, reject the null hypothesis. If the test statistic is less than or equal to the critical value, fail to reject the null hypothesis.
5. State the conclusion. If the null hypothesis is rejected, it indicates that the outcomes of the rolled die are not equally likely. If the null hypothesis is not rejected, it suggests that the outcomes of the rolled die are equally likely.