A spinner is mounted on a piece of cardboard divided into six areas of equal size. Each of the six areas is a different color (blue, yellow, red, green, white and orange). When the spinner is spun, each color should be selected by the spinner approximately $\frac { 1 } { 6 }$ of the time. A student suspects that a certain spinner is defective. The suspected spinner is spun 90 times. The results are shown below. Calculate the chi -square test statistic $x ^ { 2 }$ to test the student's claim. Use $\alpha$=0.10 .
$\begin{array} { l | c c c c c c }
\text { Color } & \text { Blue } & \text {Yellow } &\text { Red } & \text { Green } & \text { White } & \text {Orange } \
\hline \text { Frequency } & 15 & 12 & 11 & 17 & 19 & 16
\end{array}$
A) 3.067
B) 2.143
C) 5.013
D) 4.312

Question

A spinner is mounted on a piece of cardboard divided into six areas of equal size. Each of the six areas is a different color (blue, yellow, red, green, white and orange). When the spinner is spun, each color should be selected by the spinner approximately $\frac { 1 } { 6 }$ of the time. A student suspects that a certain spinner is defective. The suspected spinner is spun 90 times. The results are shown below. Calculate the chi -square test statistic $x ^ { 2 }$ to test the student's claim. Use $\alpha$=0.10 .
$\begin{array} { l | c c c c c c } 
\text { Color } & \text { Blue  } & \text {Yellow } &\text { Red } & \text { Green }  & \text { White  } & \text {Orange } \ 
\hline \text { Frequency } & 15 & 12 & 11 & 17 & 19 & 16
\end{array}$
A)  3.067 
B)  2.143 
C)  5.013 
D)  4.312

Quizplus · Accepted Answer

The chi-square test statistic $x^2$ is calculated using the formula $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. Since each color should be selected $\frac{1}{6}$ of the time in 90 spins, the expected frequency for each color is $90 \times \frac{1}{6} = 15$. The calculation for each color is as follows:- Blue: $\frac{(15-15)^2}{15} = 0$- Yellow: $\frac{(12-15)^2}{15} = 0.6$- Red: $\frac{(11-15)^2}{15} = 1.067$- Green: $\frac{(17-15)^2}{15} = 0.267$- White: $\frac{(19-15)^2}{15} = 1.067$- Orange: $\frac{(16-15)^2}{15} = 0.067$Adding these values together gives $\chi^2 = 0 + 0.6 + 1.067 + 0.267 + 1.067 + 0.067 = 3.067$.

A Spinner Is Mounted on a Piece of Cardboard Divided 16\frac { 1 } { 6 }61​

A Spinner Is Mounted on a Piece of Cardboard Divided $\frac { 1 } { 6 }$