Question

** Show all necessary work, and round final answers to three places – all problems can be answered without rounding intermediate steps.**

1. Goodness of Fit – Vending Machines: The Coca-Cola vending machines on the UK campus typically offer six drink options: Coca-Cola, Diet Coke, Coke Zero, Cherry Coke, Mello Yello, and Dasani. Suppose a random sample of 300 credit card transactions at a particular vending machine was taken, and the distribution of drinks sold during those transactions is below.

Drink	Coca-Cola	Diet Coke	Coke Zero	Cherry Coke	Mello Yello	Dasani
Observed	63			44	38	55

The two missing values add up to 100. The value you should use for the observed number of Diet Cokes purchased is based on your table number, and can be found on the fourth page of this document. The observed number of Coke Zeroes purchased can then be found by subtracting the observed number of Diet Cokes purchased from 100. (For example, if there are 35 Diet Cokes in the sample, there are 65 Coke Zeroes. If there are 70 Diet Cokes, there are 30 Coke Zeroes, etc.)


Suppose we want to determine if there is evidence that the six drinks are not equally preferred. So the null and alternative hypotheses are:

?0: The six drinks are equally preferred.      vs.      ??: The six drinks are not equally preferred.  


Complete the chi-squared goodness-of-fit test by doing the following: (a) Determine the expected counts and compute the test statistic. (If the drinks are equally preferred, the expected counts will all be equal.) If you want to round the components, round them to at least three places.

(b) Compute the p-value using the theoretical ?2 distribution on StatKey. (Don’t use anything under “More Advanced Randomization Tests”.) Copy a screenshot of the p-value into your assignment, and make sure you don’t crop the degrees of freedom out.

(c) If the significance level is ? = .05, which of the following is the correct conclusion? 1. ?0 should be rejected. There is sufficient evidence to conclude that the six drinks are not equally preferred. 2. ?0 should not be rejected. There is insufficient evidence to conclude that the six drinks are not equally preferred.

Answer 1