Is astrology scientific? The General Social Survey (GSS) asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education:

a. State appropriate hypotheses for performing a chi-square test for independence in this setting.

b. Compute the expected counts assuming that $H_0$is true.

c. Calculate the chi-square test statistic, df, and P-value.

d. What conclusion would you draw?

We need to find out the appropriate hypothesis for performing a chi-square test for independence in this setting.

We know that

The null hypothesis asserts that the variables are unrelated, whereas the alternative hypothesis asserts that they are.

$H_0$is there is no association between degree held and the opinion about the astrology.

$H_{\alpha }$is there is an association between degree held and the opinion about the astrology.

We need to find the expected counts.

From part (a)

We know that

Expected frequencies are a product of row and column total divided by table total. So,

We need to find the test statistics, df, P-value.

From parts (a) and (b)

We know that

The squared differences between the actual and predicted frequencies, divided by the expected frequency, make up the chi-square subtotals.

Therefore, test-statistics is, ${\chi }^2=10.5819$

And,

$$\begin{gathered} df=2 \\ P-value=0.005<P<0.01=0.005037 \end{gathered}$$

We need to find out the conclusion drawn.

From the parts (a) ,(b) and (c)

We know that

There are many convincing pieces of evidence for the association between degree held and the opinion about astrology.

And this is the conclusion we drew.