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) Null hypothesis : There is no association between the type of phone used by an individual and type of response from the individual.

In other words, The type of phone used by an individual is independent of type of response from the individual

Alternative hypothesis : There is association between the type of phone used by an individual and type of response from the individual.

Or, The type of phone used by an individual is dependent of type of response from the individual.

B) Here, we have 3*2 contingency table -

	Mobile	Landline
No Answer	552	42
Voicemail	3347	2843
Person answers phone	8399	8612

Degrees of freedom = (number of rows - 1)*(number of columns - 1) = (3-1)*(2-1) = 2*1 = 2

Critical value of chi square with 2 degrees at 10% level of significance for two tailed test is - lower critical value = 0.103 [It can be obtained from the chi square table by finding the value corresponding to 2 degrees of freedom and 0.95 probability (since it is two tailed, so, 0.05 probability on both sides)]

Upper critical value = 5.991 [It can be obtained from the chi square table by finding the value corresponding to 2 degrees of freedom and 0.05 probability]

C) Now, Calculated chi square = 145.13

The lower critical value =0.103 and upper critical value = 5.991.

So, our rejection region is given by -

chi square < 0.103 and chi square > 5.991

Hence, the acceptance region will be :

0.103 < chi square < 5.991

Since, the calculated chi square value lies outside the acceptance region, that is in the rejection region (chi square > 5.991)

Hence, null hypothesis may be rejected at 0.10 level of significance, so, we conclude that the type of phone used by an individual is dependent of the type of response from the individual.