The accompanying data on degree of spirituality for a sample of natural scientists and a sample of social scientists working at research universities appeared in a paper. assume that it is reasonable to regard these two samples as representative of natural and social scientists at research universities. is there evidence that the spirituality category proportions are not the same for natural and social scientists? test the relevant hypotheses using a significance level of 0.01. degree of spirituality very moderate slightly not at all natural scientists 54 161 195 216 social scientists 55 220 239 242 x² = p-value=

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:

=∑∑

Where:

: Observed value (the ones we have in our table)

: Expected value

The expected value of every observation (ij) is calculated as it follows:

Where,

: marginal total by rows

: 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 by first calculating 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

We may consider our null hypothesis as it follows:

The degree of spirituality category proportions are the same for natural and social scientists.

To prove this we have:

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.