Question

A restaurant has dishes A, B, C, D, E, F and G

The owners anticipate that dishes will be ordered in the following proportions: 30% (A), 15% (B), 20% (C), 5% (D), 8% (E), 12% (F) and 10% (G). The number of orders placed during the first two days of business was 75 (A), 60 (B), 50 (C), 14 (D), 20 (E), 40 (F), and 41 (G).

   State and conduct the appropriate hypothesis test to determine whether there is sufficient evidence at the .05 significance level to conclude the owners’ anticipation is incorrect. What is the p-value associated with the test statistic? (Place bounds on the p-value if necessary.)

Answer 1

Null hypothesis:Ho:  owners’ anticipation is correct about  proportions of order of dishes

Alternate hypothesis:Ha: owners’ anticipation is incorrect about  proportions of order of dishes

degree of freedom =categories-1=

6

for 0.05 level and 6 degree of freedom :rejection region =

12.592

applying chi square test of goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.300	75	90.00	-1.58	2.500
B	0.150	60	45.00	2.24	5.000
C	0.200	50	60.00	-1.29	1.667
D	0.050	14	15.00	-0.26	0.067
E	0.080	20	24.00	-0.82	0.667
F	0.120	40	36.00	0.67	0.444
G	0.100	41	30.00	2.01	4.033
total	1.000	300	300		14.378

as test statistic X² =14.378 is higher than critical value we reject null hypothesis and conclude that  owners’ anticipation is incorrect about  proportions of order of dishes

bound of p values 0.025 < p value <0.05