The goal of this exercise is to assess your understanding of the chi square test. Please read the problem carefully and answer the question. Good luck!

Assume you have data below that displays the number of students who elect different undergraduate majors. Number of Students Selecting Different Majors
| |Computer Sciences |English Literature | | | |
|Pre-Med | | |Education |Engineering |Total |
|50 |85 |25 |60 |80 |300 |

We want to know whether those numbers differ due to chance. In other words, at 0.01 level of confidence, are some majors selected more often than others, or is the selection pattern essentially random? The null hypothesis is that the programs are equally preferred.

Create a table that shows the computation of the Chi Square statistic [6 POINTS]. Use a decision rule to determine whether the null hypothesis is rejected or not [4 POINTS].

Solution:
Ho: The majors are equally preferred (probability of liking each major = 1/5).
HA: The majors are not equally preferred.

(Using the Chi Square Statistic to evaluate to what extent the hypothesis and data have a good fit.

[pic]

Where, Oi is actual frequency observed in cell i Ei is the expected frequency in cell i K is the number of cells in table.

(Expected frequency (Ei =10 i.e., 300 people with equal chance of selecting any one of the five majors).
(Here, K= 5 (number of majors), hence degree of freedom is 4 (degree of freedom = K-1)

(Calculating the E value in Excel:

|Oi |Ei ||Oi-Ei| |(Oi-Ei)^2 |(Oi-Ei)^2/Ei |
|50 |60 |10 |100 |1.667 |
|85 |60 |25 |625 |10.417 |
|25 |60 |35 |1225 |20.417 |
|60 |60 |0 |0 |0 |
|80 |60 |20 |400 |6.667 |
| |Calculated [pic] |39.168 |
| |Critical [pic] |13.277 |

(Now, using the decision rule:

If [pic]calculated >= [pic]critical, reject the null.
In our case [pic]calculated = 39.168 [pic]critical = 13.277 (From chi-square distribution table)

( Hence we Reject the NULL. That means that the majors are not equally favored. Some majors selected more often than others.