Question

Please help me with the follow: *ALSO Please show all work so I may follow along* Thank you!

A multinomial experiment with k = 3 cells and n= 400 produced the data shown in the accompanying table. Do these data provide sufficient evidence to contradict the null hypothesis that p1 = .50, p2 = .25, and p3 = .25? Test, using a = .05.

A multinomial experiment with k = 3 cells and n = 400 produced the data shown in the accompanying table. Do these data provide sufficient evidence to contradict the null hypothesis that P1 = .50, P2 = 25, and P3 = .25? Test, using a = .05. 1 228 Cell 2 80 3 92 ni

Please help me with the follow: *ALSO Please show all work so I may follow along* Thank you!

Answer 1

We use chi square test for goodness of fit

Test statistic

آج =ک (0 - GI)

where Oi : observed frequency

Ei : expected frequency under the null hypothesis

Expected frequency calculation

Cell	pi	Ei=400*pi
1	0.5	200
2	0.25	100
3	0.25	100

Calculation of Chi square

	Oi	Ei	(Oi-Ei)^2/Ei
	228	200	3.92
	80	100	4
	92	100	0.64
total			8.56

Thus

$1587094996674_blob.png$ 8.56

df = 3-1 =2

Critical value of chi square at  a=0.05 with 2 df

$1587094996680_blob.png$ 5.99 (from chi square table)

Since calculated value of $1587094997284_blob.png$ > 5.99

We reject H0

There is sufficient evidence to contradict the null hypothesis p1= 0.50 , p2=0.25 , p3=0.25