A die,suspected of being unfair,was rolled 50 times.The number of times each face appeared was recorded in the following table. $$\begin{array} { c | c }
\text { Face } & \text { Count } \
\hline 1 & 8 \
2 & 10 \
3 & 9 \
4 & 11 \
5 & 5 \
6 & 7
\end{array}$$
A)Homogeneity
B)Goodness-of-fit
C)Independence

Question

A die,suspected of being unfair,was rolled 50 times.The number of times each face appeared was recorded in the following table. $$\begin{array} { c | c } 
\text { Face } & \text { Count } \
\hline 1 & 8 \
2 & 10 \
3 & 9 \
4 & 11 \
5 & 5 \
6 & 7
\end{array}$$
A)Homogeneity
B)Goodness-of-fit
C)Independence

Quizplus · Accepted Answer

The table shows the observed frequencies of each face, and we can compare these with the expected frequencies if the die was fair. Since there are six faces and 50 rolls, we expect each face to appear 50/6 = 8.33 times on average. A goodness-of-fit test can be used to determine if the observed frequencies differ significantly from the expected frequencies. The null hypothesis is that the die is fair, and we can use a chi-squared test to calculate the test statistic and p-value. If the p-value is less than the significance level (e.g., 0.05), we would reject the null hypothesis and conclude that the die is unfair. Therefore, B is the best choice for this scenario.

A Die,suspected of Being Unfair,was Rolled 50 Times Face Count 18210394115567\begin{array} { c | c } \text { Face } & \text { Count } \\\hline 1 & 8 \\2 & 10 \\3 & 9 \\4 & 11 \\5 & 5 \\6 & 7\end{array} Face 123456​ Count 81091157​​

A Die,suspected of Being Unfair,was Rolled 50 Times $\begin{array} { c | c } \text { Face } & \text { Count } \\\hline 1 & 8 \\2 & 10 \\3 & 9 \\4 & 11 \\5 & 5 \\6 & 7\end{array}$