Suspecting that a die may be unfair,you want to investigate.To check,you roll it 36 times,recording the number of times each face appears. $$\begin{array} { l | l }
\text { Face } & \text { Count } \
\hline 1 & 6 \
2 & 10 \
3 & 4 \
4 & 8 \
5 & 4 \
6 & 4
\end{array}$$ To see if these results are unusual,will you test goodness-of-fit,homogeneity,or independence?
A)Independence
B)Goodness-of-fit
C)Homogeneity

Question

Suspecting that a die may be unfair,you want to investigate.To check,you roll it 36 times,recording the number of times each face appears. $$\begin{array} { l | l } 
\text { Face } & \text { Count } \
\hline 1 & 6 \
2 & 10 \
3 & 4 \
4 & 8 \
5 & 4 \
6 & 4
\end{array}$$ To see if these results are unusual,will you test goodness-of-fit,homogeneity,or independence?
A)Independence
B)Goodness-of-fit
C)Homogeneity

Quizplus · Accepted Answer

The best choice for this scenario is to test the goodness-of-fit. Goodness-of-fit tests are used to determine if a given sample fits a particular distribution. In this case, we want to see if the results of rolling the die fit the expected distribution of a fair die. The chi-squared goodness-of-fit test can be used to compare the observed frequencies (number of times each face appears) with the expected frequencies (assuming a fair die) and determine if they are significantly different. Therefore, the correct answer is B.

Suspecting That a Die May Be Unfair,you Want to Investigate Face Count 1621034485464\begin{array} { l | l } \text { Face } & \text { Count } \\\hline 1 & 6 \\2 & 10 \\3 & 4 \\4 & 8 \\5 & 4 \\6 & 4\end{array} Face 123456​ Count 6104844​​

Suspecting That a Die May Be Unfair,you Want to Investigate $\begin{array} { l | l } \text { Face } & \text { Count } \\\hline 1 & 6 \\2 & 10 \\3 & 4 \\4 & 8 \\5 & 4 \\6 & 4\end{array}$