A Multinomial Experiment with K = 4 Cells and N $p _ { 1 } = p _ { 2 } = p _ { 3 } = p _ { 4 } = .25$

Multiple Choice

A multinomial experiment with k = 4 cells and n = 400 produced the data shown in the following table.


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) $( 0.489,0.586 )$
B) $( 0.496,0.579 )$
C) $( 0.495,0.580 )$
D) $( 0.086,0.149 )$