Question

Question 14

Please answer the following set of questions, based on the information provided below.

A service company is curious to know whether customer age is crucial in deciding to subscribe. The company has collected a random sample of 1000 people, and asked everyone whether he or she would subscribe to the service. The company knows which age group the person falls into: under 18 years of age, 18 - 29 years of age, 30-45 years of age and 46 years or older. The company decides to use a chi-square test of independence at 0.05 level of significance to answer its questions. Below are the sample’s data:

                                                              

	Under 18	18-29	30-45	46 or older	Total
Yes	160	220	150	120	650
No	70	110	90	80	350
Total	230	330	240	200	1000

What is the degrees of freedom (df) for this test?

Answer 1

Here the answer can be stated in below way. Before that, I would like to have a clear idea about the chi-square test of independence.

Suppose that Variable A has r levels, and Variable B has c levels. The null hypothesis states that knowing the level of Variable A does not help you predict the level of Variable B. That is, the variables are independent.

H_o: Variable A and Variable B are independent.

H_a: Variable A and Variable B are not independent.

The alternative hypothesis is that knowing the level of Variable A can help you predict the level of Variable B.

Note: Support for the alternative hypothesis suggests that the variables are related; but the relationship is not necessarily causal, in the sense that one variable "causes" the other.

• Degrees of freedom. The degrees of freedom (DF) is equal to:

  DF = (r - 1) * (c - 1)

  where r is the number of levels for one categorical variable, and c is the number of levels for the other categorical variable.

Here, in this case, the YES group, as well as the NO group, have 4 categories. Hence the DF will be

(4-1)*(4-1) = 9

Thanks!!