A die is rolled 180 times and the following data are obtained.Is the die fair? Number Frequency
1 31
2 34
3 26
4 16
5 32
6 41
A)H0: The die is not fair. HA: The die is fair (all numbers occur with equal frequency).
Conclusion: Do not reject the null hypothesis.There is insufficient evidence to claim that the numbers on the die do not occur with equal frequency.
B)H0: The die is not fair. HA: The die is fair (all numbers occur with equal frequency).
Conclusion: Do not reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency.
C)H0: The die is fair (all numbers occur with equal frequency). HA: The die is not fair.
Conclusion: Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that the die is loaded.
D)H0: The die is fair (all numbers occur with equal frequency). HA: The die is not fair.
Conclusion: Reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency.
E)H0: The die is not fair. HA: The die is fair (all numbers occur with equal frequency).
Conclusion: Reject the null hypothesis.There is sufficient evidence to claim that the numbers on the die do not occur with equal frequency.

Question

Quizplus · Accepted Answer

The correct hypothesis setup for testing fairness is to assume fairness as the null hypothesis (H0: the die is fair) and unfairness as the alternative hypothesis (HA: the die is not fair). The given frequencies show significant variation from the expected frequency (180/6 = 30 for each number if the die were fair), suggesting the die may not be fair, leading to the rejection of the null hypothesis.

A Die Is Rolled 180 Times and the Following Data