Question

A national youth organization sells six different kinds of cookies during its annual cookie campaign. A local leader is curious about whether national sales of the six kinds of cookies are uniformly distributed. He randomly selects the amounts of each kind of cookies sold by five youths and combines them into the observed data that follow. Use α = .05 to determine whether the data indicate that sales for these six kinds of cookies are uniformly distributed.

Kind of Cookie	Observed Frequency
Chocolate chip	191
Peanut butter	168
Cheese cracker	155
Lemon flavored	161
Chocolate mint	211
Vanilla filled	165

Appendix A Statistical Tables

(Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Observed χ2 =  
Cookie Sales is                                                           uniformly distributednot uniformly distributed by kind of cookie.

Answer 1

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.167	191.000	175.167	1.20	1.431
2	0.167	168.000	175.167	-0.54	0.293
3	0.167	155.000	175.167	-1.52	2.322
4	0.167	161.000	175.167	-1.07	1.146
5	0.167	211.000	175.167	2.71	7.330
6	0.167	165.000	175.167	-0.77	0.590
total	1.000	1051	1051		13.1123
Observed test statistic X2 =		13.11

p value =

0.0223

since p value is less than 0.05 ;

Cookie Sales is not uniformly distributed by kind of cookie.