Question

A null hypothesis for a goodness-of-fit test and a frequency table from a sample are given.

H 0 :   p a = 0.1 , p b = 0.34 ,   p c = 0.2 , p d = 0.16 , p e = 0.1 , p f = 0.1
H a : Some p i is wrong

A	B	C	D	E	F
203	862	531	438	212	154

(a) Find the expected count for the category labeled B.

The expected count is Enter your answer in accordance to item (a) of the question statement.


(b) Find the contribution to the sum of the chi-square statistic for the category labeled B.

Round your answer to three decimal places.

The contribution for the category labeled B is Enter your answer in accordance to item (b) of the question statement.

(c) Find the degrees of freedom for the chi-square distribution for this table.

Enter your answer in accordance to item (c) of the question statement degree(s) of freedom

  

Answer 1

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
Category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
1	0.1000	203	240.00		5.704
2	0.3400	862	816.00		2.593
3	0.2000	531	480.00		5.419
4	0.1600	438	384.00		7.594
5	0.1000	212	240.00		3.267
5	0.1000	154	240.00		30.817
total	1.00	2400	2400		55.39
test statistic X2=		55.393

from above:

a)

expected count for the category labeled B =816

b)

contribution to the sum of the chi-square statistic for the category labeled B =2.593

c)

degree of freedom =categories-1=

5