Question

Chi-square test.

The past output of a machine indicates that each unit it produces will be

P(top grade) = 40% P(high grade) = 30%

P(medium grade) = 20% P(low grade) = 105

A new machine produces 500 units and shows the following results

Top = 234 high =117 medium = 81 and low = 68

Can the difference in output be solely due to chance?

Answer 1

null hypothesis: Ho: P(top grade) = 40% ,P(high grade) = 30%; P(medium grade) = 20% ;P(low grade) = 10%

Alternate hypothesis:Ha: at least one of above proportion differs,

degree of freedom =categories-1=

3

for 0.05 level and 3 degree of freedom :rejection region =

7.815

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Top	0.400	234	200.00	2.40	5.780
high	0.300	117	150.00	-2.69	7.260
Medium	0.200	81	100.00	-1.90	3.610
Low	0.100	68	50.00	2.55	6.480
total	1.000	500	500		23.130

as test statistic=23.130 is significantly high than critical value we reject null hypothesis

we have sufficient evidence to conclude that difference in output can not be solely due to chance