Question

a researched is interested in determining if the proportion of children that collect specific types of toys is equal. to test, he takes a random sample of 500 children and finds that 36% of them collect legos, 19% of them collect beanie babies 18% of them collect webkins and 27% collect hot wheels. at the 10% significance level, what conclusions can be reached?

Answer 1

Hypothesis:

H0: P1 = P2 = P3 = P4 = 1/4 or 0.25

Ha: at least one Pi is different

Test:

Observed P	O=n*p	Expected P (1/4)	Expected = n*P	(O-E)^2/E
0.36	180	0.25	125	24.2
0.19	95	0.25	125	7.2
0.18	90	0.25	125	9.8
0.27	135	0.25	125	0.8
Total	500	1	X^2	42
n	500		df	3	n-1
alpha	0.1		X^2 critical	6.251388631	CHIINV(0.1,3)
			P value	4.01213E-09	CHIDIST(X^2 stat,3)

X^2 stat = 42

P value = 0

P value < 0.1, Reject H0

There is enough evidence to conclude that the proportion of children that collect specific types of toys is different at 10% significance level