Q. 46 - The Practice of Statistics for AP

Question

The General Social Survey 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) Make a bar graph that compares opinions about astrology for the three education categories. Describe what you see. 

(b) Minitab output for a chi-square test using these data is shown below. Carry out the test. What conclusion do you draw? 

Step-by-Step Solution

Answer

(a) The higher the degree of the subjects, the more likely that they think that astrology is not at all scientific.

(b) There is sufficient evidence that there is an association between the variables.

Part (a) Step 1: Given information

The given data is

Part (a) Step 2: Explanation

The proportions in each group is the number of subjects divided by the column total:

Create a histogram

The width of each bar is equal and the height is equal to the proportion.

Part (b) Step 1: Given information

The given data is

Part (b) Step 2: Explanation

The null hypothesis states that there is no association between the variables:

$H_0$: There is no association between the variables

The alternative hypothesis states that there is an association between the variables:

$H_a$ : There is an association between the variables

By using the test of chi-squater, we obtained that:

$x^2=10.582$

Let's find the degree of freedom:

$$\begin{gathered} =(3-1)(2-1) \\ =2\times 1 \\ =2 \end{gathered}$$

The P-value is given in the output as:

$P=0.005$

If the P-value is smaller than the significance level, reject the null hypothesis:

$P<0.05 \Rightarrow Reject H_0$