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Solution Library
State Null And Alternate Hypothesis For Testing Percentages And Probabilities
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 percentages as 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 stating null and alternate hypothesis for testing the percentages and their probabilities.
Total Word Count 98
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