Find the value of the chi-square test statistic for the goodness-of-fit test.
-You wish to test the claim that workplace accidents are distributed on workdays as follows: Monday: 25\%, Tuesday: $15 \%$, Wednesday: $15 \%$, Thursday: $15 \%$, Friday: $30 \%$. In a study of 100 workplace accidents, 24 occurred on a Monday, 15 occurred on a Tuesday, 13 occurred on a Wednesday, 14 occurred on a Thursday, and 34 occurred on a Friday. What is the value of the $\chi ^ { 2 }$ test statistic? The observed frequencies and the expected frequencies are shown below.
$\begin{array}{r|c}
\begin{array}{r}
\text { Observed } \
\text { Frequency }(\mathrm{O})
\end{array} & \begin{array}{r}
\text { Expected } \
\text { Frequency (E) }
\end{array} \
\hline 24 & 25 \
15 & 15 \
13 & 15 \
14 & 15 \
34 & 30
\end{array}$
A)$\chi ^ { 2 } = 7.333$
B) $\chi ^ { 2 } = 0.907$
C) $\chi ^ { 2 } = 0.891$
D) $\chi ^ { 2 } = 3.143$

Question

Find the value of the chi-square test statistic for the goodness-of-fit test.
-You wish to test the claim that workplace accidents are distributed on workdays as follows: Monday: 25\%, Tuesday: $15 \%$, Wednesday: $15 \%$, Thursday: $15 \%$, Friday: $30 \%$. In a study of 100 workplace accidents, 24 occurred on a Monday, 15 occurred on a Tuesday, 13 occurred on a Wednesday, 14 occurred on a Thursday, and 34 occurred on a Friday. What is the value of the $\chi ^ { 2 }$ test statistic? The observed frequencies and the expected frequencies are shown below.
$\begin{array}{r|c}
\begin{array}{r}
\text { Observed } \
\text { Frequency }(\mathrm{O})
\end{array} & \begin{array}{r}
\text { Expected } \
\text { Frequency (E) }
\end{array} \
\hline 24 & 25 \
15 & 15 \
13 & 15 \
14 & 15 \
34 & 30
\end{array}$  
A)$\chi ^ { 2 } = 7.333$
B) $\chi ^ { 2 } = 0.907$
C) $\chi ^ { 2 } = 0.891$
D) $\chi ^ { 2 } = 3.143$

Quizplus · Accepted Answer

The chi-square test statistic $\chi^2$ is calculated using the formula $\chi^2 = \sum \frac{(O - E)^2}{E}$, where $O$ is the observed frequency and $E$ is the expected frequency. Plugging in the values from the table:$$\chi^2 = \frac{(24-25)^2}{25} + \frac{(15-15)^2}{15} + \frac{(13-15)^2}{15} + \frac{(14-15)^2}{15} + \frac{(34-30)^2}{30} = \frac{1}{25} + 0 + \frac{4}{15} + \frac{1}{15} + \frac{16}{30} = 0.04 + 0 + 0.267 + 0.067 + 0.533 = 0.907.$$

Find the Value of the Chi-Square Test Statistic for the Goodness-Of-Fit