Q. 45 - The Practice of Statistics for AP

Question

Some people think recycled products are lower in quality than other products, a fact that makes recycling less practical. Here are data on attitudes toward coffee filters made of recycled paper from a random sample of adults: 

(a) Make a bar graph that compares buyers’ and non-buyers’ opinions about recycled filters. 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 bar graph is 

Buyers frequently believe that product quality is higher, but nonbuyers frequently believe that product quality is lower.

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

Part (a) Step 1: Given information

The given data is 

Part (b) Step 2: Explanation

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

Create a histogram

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

Buyers frequently believe that product quality is higher, but nonbuyers frequently believe that product quality is lower.

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

The P-value is given in the output as:

$P=0.022$

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

$P<0.05 \Rightarrow Reject H_0$

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