Answer:
There is no evidence that the spirituality category proportions are different for natural and social scientists.
Step-by-step explanation:
To solve this question we must perform a Chi square test calculating the expected values of the observed behavior.
We start by completing the table given by adding the totals:
Observed Very Moderate Slightly Not at all Total
Natural Sc 54 161 195 216 626
Social Sc 55 220 239 242 756
Total 109 381 434 458 1382
Now, the chi square value is calculated with the following formula:
[tex]x^{2}[/tex]=∑∑[tex]\frac{O_{ij}-E_{ij} }{E_{ij} }[/tex]
Where:
[tex]O_{ij}[/tex]: Observed value (the ones we have in our table)
[tex]E_{ij}[/tex]: Expected value
The expected value of every observation (ij) is calculated as it follows:
[tex]E_{ij}=\frac{n_{i}c_{j} }{N}[/tex]
Where,
[tex]n_{i}[/tex]: marginal total by rows
[tex]c_{j}[/tex]: marginal total by columns
N: Total of observations
Now, for the expected observations we obtain the following table:
Expected Very Moderate Slightly Not at all Total
Natural Sc 49.37 172.58 196.59 207.46 626
Social Sc 59.63 208.42 237.41 250.54 756
Total 109 381 434 458 1382
Having the expected values we now can calculate [tex]x^{2}[/tex] by first calculating [tex]\frac{O_{ij}-E_{ij} }{E_{ij} }[/tex] for each observation:
Chi sq Very Moderate Slightly Not at all Total
Natural Sc 0.434 0.777 0.013 0.352 1.575
Social Sc 0.359 0.643 0.011 0.291 1.304
Total 0.793 1.420 0.024 0.643 2.879
[tex]x^{2}=2.879[/tex]
We may consider our null hypothesis as it follows:
[tex]H_{0}:[/tex] The degree of spirituality category proportions are the same for natural and social scientists.
To prove this we have:
[tex]P(x^{2}\geq 2.879)[/tex]
α=0.01
α: significance level
Calculating this value with a chi square table (or with statistical software like R) we obtain:
P-value=0.4105
Because the p-value is larger than α the null hypothesis is accepted. Which means we cannot say that the spirituality category proportions are different.
