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	215
Vanilla filled	165

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

Observed χ2 =______
Cookie Sales is ________by kind of cookie.                                           

A) Uniformly distributed

B) Not uniformly distributed

Answer 1

We have to check whether the distribution is uniform or not.

Ho: Distribution is uniform

H1: Distribution is not uniform

We have six different kind of cookies, so proportion for each cookie = 1/6

total frequency = 191+168+155+161+215+165 = 1055

Expected value = proportion*total frequency = (1/6)*1055 = 175.83

Degree of freedom (df) = number of categories-1 = 6-1 = 5

Using TI 84 calculator

Press STAT then EDIT and enter the data into List 1 (observed values) and L2 (Expected value)

Again

Press STAT then TESTS and select -GOF test

Observed = L1

Expected = L2

df = 5

Calculate

we get

test statistic = 14.77

p value = 0.0114

We can see that the p value is less than significance level, i.e. 0.0114 < 0.05, so we will reject the null hypothesis. This shows that the distribution is not uniform.

Therefore, answer is

Observed χ2 = 14.77
Cookie Sales is Not uniformly distributed by kind of cookie.