Question

A marketing company wants to research whether the type of phone used by an individual is independent of the type of response from the individual. The company surveyed respondents by phone, drawing a random sample of landline telephones and another random sample of mobile phones.

There were 3 types of responses: No Answer, Voicemail and Person answers phone

	Mobile	Landline	Total
No Answer	552	42	594
Voicemail	3347	2843	6190
Person answers phone	8399	8612	17,011
Total	12,298	11,497	23,795

A) State the hypotheses to test for independence.

B) Write down the degrees of freedom AND the critical value for α = 10%.

C) You are now told that the calculated Chi square statistic value is 145.13. Use this to make your decision and AND briefly explain how you made your decision AND give your conclusion.

Answer 1

A marketing company wants to research whether the type of phone used by an individual is independent of the type of response from the individual.

To test the two attributes are independent or not we use chi- square test.

A)Hypothesis:

H0:The type of phone used by an individual is independent of the type of response from the individual.

V/ s

H1: The type of phone used by an individual is not independent of the type of response from the individual.

B) Test statistic is follow chi- square test with degrees of freedom ( m-1) (n-1) at % level of Significance.

m = number of rows=3

n = number of columns=2

Degree of freedom= (3-1)*(2-1)=2

The critical value for 2 degrees of freedom at α = 10%.=4.61

C)We are known that calculate chi- square statistic value is 145.13

Cal = 145.13

Cal > critical value

Therefore we reject the null hypothesis at 10 % level of Significance. i.e.we accept the null hypothesis.

Conclusion:

We can conclude that the type of phone used by an individual is not independent of the type of response from the individual.