Answer to Question #147178 in Statistics and Probability for Adam

Question

Zane is interested in the proportion of people who recycle each of three distinct products: paper, plastic, and electronics. He wants to test the hypothesis that the proportion of people recycling each type of product differs by age group: 12-18 years old, 19-30 years old, 31-40 years old, and over 40 years old. Suppose he found a sample χ2 = 16.83.
a. How many d.f are used? Approximate the P-value and conclude the test at the 1% level of significance. Does it appear that the proportion of people who recycle each of the specified products differ by age group? Explain.
b. From this study, can Zane identify how the different age groups differ regarding the proportion of those recycling the specified products? Explain.

Answer 1

a) χ² = 16.83

N=4

df=N-1=3

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme.

0.005<P<0.010

If the P-value is less than or equal ti the significance leven, then the null hypothesis is rejected:

P<0.01=1%, so reject H₀

There is sufficient evidence to support the claim that the variables are not independent.

b) You cannot determine how variables differ using a test of homogeneity, because the test only determines if there is a difference or not.