Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.4 , p _ { 2 } = 0.25$ $p _ { 3 } = 0.15 , p _ { 4 } = 0.1 , p _ { 5 } = 0.1$
$\begin{array} { l | l l l l l }
\text { Category } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 33 & 13 & 7 & 12 & 8
\end{array}$
Compute the expected frequencies.
A) 0.452,0.178,0.096,0.164,0.11
B) 33,13,7,12,8
C) 29.2,18.25,10.95,7.3,7.3
D) 14.6,14.6,14.6,14.6,14.6

Question

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.4 , p _ { 2 } = 0.25$ $p _ { 3 } = 0.15 , p _ { 4 } = 0.1 , p _ { 5 } = 0.1$
 $\begin{array} { l | l l l l l } 
\text { Category } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 33 & 13 & 7 & 12 & 8
\end{array}$ 
Compute the expected frequencies.
A)  0.452,0.178,0.096,0.164,0.11 
B)  33,13,7,12,8 
C)  29.2,18.25,10.95,7.3,7.3 
D)  14.6,14.6,14.6,14.6,14.6

Quizplus · Accepted Answer

To calculate the expected frequencies, multiply the total number of observations by the probability of each category under the null hypothesis. The total number of observations is $33 + 13 + 7 + 12 + 8 = 73$. Therefore, the expected frequencies are $73 \times 0.4 = 29.2$ for category 1, $73 \times 0.25 = 18.25$ for category 2, $73 \times 0.15 = 10.95$ for category 3, $73 \times 0.1 = 7.3$ for category 4, and $73 \times 0.1 = 7.3$ for category 5.

Following Are Observed Frequencies H0:p1=0.4,p2=0.25H _ { 0 } : p _ { 1 } = 0.4 , p _ { 2 } = 0.25H0​:p1​=0.4,p2​=0.25

Following Are Observed Frequencies $H _ { 0 } : p _ { 1 } = 0.4 , p _ { 2 } = 0.25$