Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2 , p _ { 3 } = 0.15$, $p _ { 4 } = 0.15 , p _ { 5 } = 0.15$.

$\begin{array}{l|lllll}
\text { Category } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 32 & 37 & 7 & 23 & 4
\end{array}$

Compute the value of $\chi ^ { 2 }$.
A) 31.667
B) 11.070
C) 9.488
D) 30.308

Question

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2 , p _ { 3 } = 0.15$, $p _ { 4 } = 0.15 , p _ { 5 } = 0.15$.

$\begin{array}{l|lllll}
\text { Category } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 32 & 37 & 7 & 23 & 4
\end{array}$

Compute the value of $\chi ^ { 2 }$.
A) 31.667
B) 11.070
C) 9.488
D) 30.308

Quizplus · Accepted Answer

The chi-square statistic is calculated using the formula $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ are observed frequencies and $E_i$ are expected frequencies. The expected frequencies are calculated based on the null hypothesis proportions and the total number of observations. After calculating, the chi-square value is approximately 30.308.

Following Are Observed Frequencies H0:p1=0.35,p2=0.2,p3=0.15H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2 , p _ { 3 } = 0.15H0​:p1​=0.35,p2​=0.2,p3​=0.15

Following Are Observed Frequencies $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2 , p _ { 3 } = 0.15$