4 8 Vending machines on a college campus offer a variety of

4. [8] Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table. Drink Type/Flavor Lemon Lime Sports Drink Kiwi Strawberry Tropical Punch Grape Sports Drink Purchase Frequency 159 198 174 149 Conduct the hypothesis test indicated by this scenario. You may use technology, but make sure you include all important information (hypotheses, test statistic, p-value, statistical conclusion using = 0.05, and practical conclusion.)

Solution

H0: Each type of drink is equally preferred by students
Ha: Not all of the preferences are equal.

Flavor -- Freq
Lemon - 159
KIwi------ 198
Punch----174
Grape-----149

If the null hypothesis were true, the expected frequencies would all be 680/4 = 170.

(ii) The test statistic is the chi-squared statistic = [O(i) -E(i) )^2 /E(i)

= (159-170)^2/170+(198-170)^2/170+(174-170...
= 8.0117

Look up the chi-squared table with 3 degrees of freedom (4 types of drinks).
p-value < 0.05
Exact p-value (calculator required) = 0.045771

(iii)
At = .05, the null hypothesis is rejected in favor of the alternative that the average number of drinks is not the same for at least two of the flavors.