Question

Does buying CDs depend on whether you own a smartphone or not? A survey asks a group of students if they buy CDs or not. It also asks if the students own a smartphone or not. The data are recorded in the contingency table below, and a chi-square Test of Independence at the 5% significance level is performed.

SmartphoneNo SmartphoneColumn TotalCDs12.269.81622No CDs17.82414.2832Row Total302454

(a) The null and alternative hypotheses are:

• H0: The two variables are independent, so owning a smartphone does not affect buying CDs.
• Ha: The two variables are dependent, so owning a smartphone does affect buying CDs.

(b)  χ20=11.9

(c)  χ20.05=3.841

(d)  What conclusions can be made? Select all that apply.

Select all that apply:

• We should reject H0.

• We should not reject H0.

• At the 5% significance level, there is not sufficient evidence to conclude that owning a smartphone affects buying CDs.

• At the 5% significance level, there is sufficient evidence to conclude that owning a smartphone affects buying CDs.

FEEDBACK

Answer 1

Given:

The null and alternative hypotheses are:

• H0: The two variables are independent, so owning a smartphone does not affect buying CDs.
• Ha: The two variables are dependent, so owning a smartphone does affect buying CDs.

(b)  χ20 = 11.9

(c)  χ20.05 = 3.841

d) The test statistics of χ2 is greater than the critical value 3.841.

So,

We should reject H0. At the 5% significance level, there is sufficient evidence to conclude that owning a smartphone affects buying CDs.