Question

a fast food resturant owner believes that when a customer orders a drink 50% will order a regular soda, 30% will order a diet soda and 20% will order water. during the day 119 customers order drinks, 53 regular drinks, 45 diet soda and 21 ordered water. using a 0.10 level of signifiicance is there sufficient evidence to conclude that the owners beliefs are incorrect?

Answer 1

Null hypothesis: Ho ":Sample data is distributed as claimed by owner

Alternate hypothesis: Ha ":Sample data is not distributed as claimed by owner

degree of freedom =categories-1=			2
for 0.1 level and 2 df :crtiical value X2 =				4.605
Decision rule: reject Ho if value of test statistic X2>4.605

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	0.500	53	59.50		0.710
2	0.300	45	35.70		2.423
3	0.200	21	23.80		0.329
total	1.000	119	119		3.4622
test statistic X2 =		3.462

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that the owners beliefs are incorrect