Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.45 , p _ { 2 } = 0.25$ $p _ { 3 } = 0.2 , p _ { 4 } = 0.05 , p _ { 5 } = 0.05$
$\begin{array} { l | l l l l l }
\text { Category } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 59 & 32 & 12 & 22 & 23
\end{array}$
Compute the value of $\chi ^ { 2 }$
A) 11.070
B) 9.488
C) 76.082
D) 73.700

Question

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.45 , p _ { 2 } = 0.25$ $p _ { 3 } = 0.2 , p _ { 4 } = 0.05 , p _ { 5 } = 0.05$
$\begin{array} { l | l l l l l } 
\text { Category } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 59 & 32 & 12 & 22 & 23
\end{array}$
Compute the value of $\chi ^ { 2 }$
A)  11.070 
B)  9.488 
C)  76.082 
D)  73.700

Quizplus · Accepted Answer

The chi-square statistic is calculated by summing $(O_i - E_i)^2 / E_i$ for each category, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. The expected frequencies are calculated using the given proportions and the total number of observations. The calculated chi-square value is approximately 73.700.

Following Are Observed Frequencies H0:p1=0.45,p2=0.25H _ { 0 } : p _ { 1 } = 0.45 , p _ { 2 } = 0.25H0​:p1​=0.45,p2​=0.25

Following Are Observed Frequencies $H _ { 0 } : p _ { 1 } = 0.45 , p _ { 2 } = 0.25$