Each side of a standard six-sided die should appear approximately $$\frac { 1 } { 6 }$$ oof the time when the die is rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below.
Calculate the chi-square test statistic χ $$x ^ { 2 }$$ to test the playerʹs claim. $$\begin{array} { l | c c c c c c }
\text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Frequency } & 15 & 12 & 16 & 19 & 17 & 11
\end{array}$$
A)3.067
B)2.143
C)5.013
D)4.312

Question

Each side of a standard six-sided die should appear approximately $$\frac { 1 } { 6 }$$ oof the time when the die is rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below.
Calculate the chi-square test statistic χ $$x ^ { 2 }$$ to test the playerʹs claim. $$\begin{array} { l | c c c c c c } 
\text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Frequency } & 15 & 12 & 16 & 19 & 17 & 11
\end{array}$$
A)3.067
B)2.143
C)5.013
D)4.312

Quizplus · Accepted Answer

The chi-square test statistic is calculated as:$$\chi^2 = \sum_{i=1}^n \frac{(O_i - E_i)^2}{E_i}$$where O_i is the observed frequency, E_i is the expected frequency, and n is the number of categories.In this case, the expected frequency for each category is 90/6 = 15.Therefore, the chi-square test statistic is:$$\chi^2 = \frac{(15 - 15)^2}{15} + \frac{(12 - 15)^2}{15} + \frac{(16 - 15)^2}{15} + \frac{(19 - 15)^2}{15} + \frac{(17 - 15)^2}{15} + \frac{(11 - 15)^2}{15} = 3.067$$Therefore, the correct answer is A.

Each Side of a Standard Six-Sided Die Should Appear Approximately 16\frac { 1 } { 6 }61​

Each Side of a Standard Six-Sided Die Should Appear Approximately $\frac { 1 } { 6 }$