A Multinomial Experiment with K = 4 Cells and N $\quad$

Short Answer

A multinomial experiment with k = 4 cells and n = 400 produced the data shown in the following table. $\quad$ $\quad$ $\quad$$\text { Cell }$
$\begin{array}{l}\begin{array}{l|rccr} & 1 & 2 & 3 & 4 \\\hline n_{i} & 47 & 206 & 104 & 43\end{array}\end{array}$
Previous studies in this area have shown that $p _ { 1 } = p _ { 2 } = p _ { 3 } = p _ { 4 } = .25$ . Construct a $95 \%$ confidence interval for the multinomial probability associated with cell 2.
A) $( 0.466,0.564 )$
B) $( 0.474,0.556 )$
C) $( 0.086,0.149 )$
D) $( 0.473,0.557 )$