A Die Is Rolled 180 Times and the Following Data

question 8

Multiple Choice

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.

---

Definitions:

Crepitus

A crackling or popping sound or sensation in the joints, skin, or lungs, often associated with arthritis or pulmonary issues.

Anterior Chest Wall

The front part of the chest that includes skin, muscles, bones, and other tissues protecting the heart and lungs.

Atelectatic Crackles

Fine crackling sounds heard through a stethoscope, often indicating incomplete expansion or collapse of lung tissue (atelectasis).

Fine Crackles

A series of short, discontinuous sounds heard during lung auscultation, often indicative of fluid in the airways.