Question

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?

Short answer

(a) The appropriate hypothesis is the null hypothesis.

(b) The expected count is,

	ASSOCIATE'S	BACHELOR'S	MASTER'S
YES	$183.59$	$251.85$	$103.56$
NO	$50.41$	$69.15$	$28.44$

c) The test statistics is ${\chi }^2=10.5819,df=2,P-value=0.005037$

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

Step-by-step solution

Part (a) Step 1: Given information 

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

Part (a) Step 2: Explanation 

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.

Part (b) Step 1: Given information 

We need to find the expected counts.

Part (b) Step 2: Explanation 

From part (a)

We know that

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

ROW AND COLUMN NUMBER	EXPECTED FREQUENCY
$E_{11}$	$183.59$
$E_{12}$	$251.85$
$E_{13}$	$103.56$
$E_{21}$	$50.41$
$E_{22}$	$69.15$
$E_{23}$	$28.44$

Part (c) Step 1: Given information 

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

Part (c) Step 2: Explanation 

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,

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

Part (d) Step 1: Given information 

We need to find out the conclusion drawn.

Part (d) Step 2: Explanation 

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.