You roll a die 48 times with the following results.Is the die fair? $141321234\begin{array} { c | r | r | r | r | r | r } \text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Frequency } & 14 & 13 & 2 & 12 & 3 & 4\end{array}$

A) 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.
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.There is insufficient evidence to claim that the numbers on the die do not occur with equal frequency.
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: Do not reject the null hypothesis.There is insufficient evidence to claim that the numbers on the die do not occur with equal frequency.

Question

You roll a die 48 times with the following results.Is the die fair?

141321234\begin{array} { c | r | r | r | r | r | r } \text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Frequency } & 14 & 13 & 2 & 12 & 3 & 4\end{array}

A) 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.
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.There is insufficient evidence to claim that the numbers on the die do not occur with equal frequency.
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: Do not reject the null hypothesis.There is insufficient evidence to claim that the numbers on the die do not occur with equal frequency.

Jashan Dhillon · Accepted Answer

Final Answer : D, Explanation :  The hypothesis test should be set up as H0: The die is fair (all numbers occur with equal frequency) and HA: The die is not fair. Then, a chi-squared goodness-of-fit test can be conducted using the observed frequencies and expected frequencies (which would be 8 for each number) to determine if there is enough evidence to reject the null hypothesis. If the test statistic exceeds the critical value, the null hypothesis is rejected, indicating that the die is not fair. The correct answer is choice D, which states that the null hypothesis is rejected and there is sufficient evidence to claim that the numbers on the die do not occur with equal frequency.

Definitions

Learning Objectives

Learning Objectives

Related questions