Question

The following table catagorizes the frequency of responses to the​ question, "How much of your communication is via​ text, mobile​ phone, or​ internet?", by age group.

​Answer/Age	18​ - 29	30​ - 49	50​ - 69	70​ +
All or most of it	136	249	188	59
About half of it	43	86	96	40
Some or none of it	23	59	121	59

Is there a relationship between the​ variables? Perform a significance test at the

alpha equals 0.01α=0.01

level and answer the following​ questions:

a. Name the variables.

b. State the null and the alternative hypothesis for the test.

c. Name the​ test, list the test​ statistic, the​ p-value and the degrees of freedom for the test.

d. State the conclusion of the test in context of the problem.

Answer 1

Answer a. The two categorical variables are the Age-groups and Categories of Time spent on communication via text, mobile phone or internet

Answer b.

Null Hypothesis, Ho: There is no difference in the amount of Time spent on communication via text, mobile phone or internet with respect to age-group.

Alternative Hypothesis, Ha: There is significant difference in the amount of Time spent on communication via text, mobile phone or internet with respect to age-group.

Answer c.

We will use Chi-Square Test of Independence

Test-Statistics is given as:

  

Here, r = 3 and c =4

Calculations:

Test - Statistics = 72.0083

degrees of freedom = 2*3 = 6

Answer d.

Conclusion: SInce, p-value < 0.01 so we reject Ho and conclude There is significant difference in the amount of Time spent on communication via text, mobile phone or internet with respect to age-group.