Suspecting that a die may be unfair,you want to investigate.To check,you roll it 90 times,recording the number of times each face appears. $$\begin{array} { l | l }
\text { Face } & \text { Count } \
\hline 1 & 15 \
2 & 25 \
3 & 10 \
4 & 20 \
5 & 10 \
6 & 10
\end{array}$$ State your hypotheses.
A)H0: The die is not fair. HA: The die is fair (all faces have p = 1/6).
B)H0: The die is not fair. HA: The die is fair (all faces have p = 1/2).
C)H0: The die is fair (all faces have p = 1/6). HA: The die is not fair.
D)H0: The die is fair (all faces have p = 1/3). HA: The die is not fair.
E)H0: The die is not fair. HA: The die is fair (all faces have p = 1/3).

Question

Suspecting that a die may be unfair,you want to investigate.To check,you roll it 90 times,recording the number of times each face appears. $$\begin{array} { l | l } 
\text { Face } & \text { Count } \
\hline 1 & 15 \
2 & 25 \
3 & 10 \
4 & 20 \
5 & 10 \
6 & 10
\end{array}$$ State your hypotheses.
A)H0: The die is not fair. HA: The die is fair (all faces have p = 1/6).
B)H0: The die is not fair. HA: The die is fair (all faces have p = 1/2).
C)H0: The die is fair (all faces have p = 1/6). HA: The die is not fair.
D)H0: The die is fair (all faces have p = 1/3). HA: The die is not fair.
E)H0: The die is not fair. HA: The die is fair (all faces have p = 1/3).

Quizplus · Accepted Answer

The null hypothesis (H0) should always be the assumption that is tested against the alternative hypothesis (HA). In this case, the null hypothesis should be that the die is fair (all faces have equal probability of showing up). The alternative hypothesis can be either that the die is not fair or that it has specific biased probabilities for certain faces. Option C is the correct choice because it assumes that the die is fair (H0: all faces have p=1/6) and the alternative hypothesis is that it is not. The other options are not appropriate because they either assume the die is biased to some specific probability or the null and alternative hypotheses are flipped.

Suspecting That a Die May Be Unfair,you Want to Investigate Face Count 115225310420510610\begin{array} { l | l } \text { Face } & \text { Count } \\\hline 1 & 15 \\2 & 25 \\3 & 10 \\4 & 20 \\5 & 10 \\6 & 10\end{array} Face 123456​ Count 152510201010​​

Suspecting That a Die May Be Unfair,you Want to Investigate $\begin{array} { l | l } \text { Face } & \text { Count } \\\hline 1 & 15 \\2 & 25 \\3 & 10 \\4 & 20 \\5 & 10 \\6 & 10\end{array}$