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Making And Testing Hypothesis With Chi-Square Test

Question

A business analyst is studying trends related to university majors in the United States. Specifically, she is interested in the enrollment proportions for various majors, and which majors are the most popular. According to the National Center for Education Statistics (NCES), the distribution of granted degrees by program category is given in the table below.

Major

Percentage of Degrees

Business Administration (All)

19.7

Other Major

29.1

Biological and Biomedical Sciences

3.2

Social Sciences

5.2

Visual and Performing Arts

3.8

Health Science

12.7

Education

9.2

Engineering

3.5

Liberal Arts and General Studies

9.6

Psychology

4

Grand Total

100

 

The analyst finds that in the 2012 General Social Survey, the observed numbers of persons
(a total of 359) graduating with degrees in these programs are as follows:

Major

Count

Business Administration (All)

75

Other Major

95

Biological and Biomedical Sciences

8

Social Sciences

31

Visual and Performing Arts

14

Health Science

43

Education

49

Engineering

22

Liberal Arts and General Studies

13

Psychology

9

Grand Total

359

 

The analyst wants to determine if the distribution of degrees granted in 2012 differs from the distribution that NCES claims. She will use the chi-squared goodness-of-fit test.

a). State the null and alternative hypotheses that will be tested (convert the percentagesas probabilities).

b). The output from a computer program used to run the test is given below. Chi-squared test for given probabilities data: c(75, 95, 8, 31, 14, 43, 49, 22, 13, 9) X-squared = 40.6562, df = 9, p-value = 5.776e-06 Show the last two (2)--and only the last two-- calculations involved in the computation of the test statistic.

c). State the conclusion in the context of the problem, based either on the rejection region or p-value approach, at the 0.05 level.

 

Summary

The question belongs to Statistics and it discusses about making a hypothesis and using chi square test to test the hypothesis.

Total Word Count 137

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