Consider the following to answer the question(s) below:
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.

-At α = 0.05
A) We reject the null hypothesis.
B) We fail to reject the null hypothesis.
C) We conclude that the purchasing agent was not correct.
D) We reject the null hypothesis and conclude that the purchasing agent was not correct.
E) We fail to reject the null hypothesis and conclude that the purchasing agent was not correct.

Question

Consider the following to answer the question(s) below:
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.
 
-At α = 0.05
A) We reject the null hypothesis. 
B) We fail to reject the null hypothesis. 
C) We conclude that the purchasing agent was not correct. 
D) We reject the null hypothesis and conclude that the purchasing agent was not correct. 
E) We fail to reject the null hypothesis and conclude that the purchasing agent was not correct.

Quizplus · Accepted Answer

We can perform a chi-squared goodness of fit test with the null hypothesis being that the drinks are equally preferred and the alternative hypothesis being that they are not. Using the given data and a chi-squared distribution table, we can calculate the test statistic to be 10.381 with 5 degrees of freedom. The critical value at alpha = 0.05 with 5 degrees of freedom is 11.07. Since the test statistic is less than the critical value, we fail to reject the null hypothesis. However, since we failed to reject the null hypothesis, we cannot conclude that the purchasing agent was correct. Therefore, the correct answer is D) We reject the null hypothesis and conclude that the purchasing agent was not correct.

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