Question

   Group Meetings   Face-to-Face Meetings with Individuals   E-mails   Other
Generation Y   180   240   50   30
Generation X   230   165   50   55
Boomer   220   185   60   35
Mature   205   150   70   75

A newspaper reported on preferred types of office communication by different age groups. Suppose the results were based on a survey of 500 respondents in each age group. The results are​ cross-classified in the table found below. At the 0.10 level of​ significance, is there evidence of a relationship between age group and type of communication​ preferred? Calculate the test statistic

Answer 1

Null hypothesis : H_o : There is no relationship between age group and type of communication​ preferred(Age group and type of communication are independent)

Alternate Hypothesis : H_a: There is relationship between age group and type of communication​ preferred(Age group and type of communication are not independent)

Test Statistic

O : Observed Frequency

E: Expected Frequency

Observed Counts/Frequency	Group Meetings	Face-to-Face Meetings with Individuals	E-mails	Other	Row Total
Generation Y	180	240	50	30	500
Generation X	230	165	50	55	500
Boomer	220	185	60	35	500
Mature	205	150	70	75	500
Column Total	835	740	230	195	2000

E: Expected Count/Frequency	Group Meetings	Face-to-Face Meetings with Individuals	E-mails	Other
Generation Y	(500*835) / 2000	(500*740) / 2000	(500*230) / 2000	(500*195) / 2000
Generation X	(500*835) / 2000	(500*740) / 2000	(500*230) / 2000	(500*195) / 2000
Boomer	(500*835) / 2000	(500*740) / 2000	(500*230) / 2000	(500*195) / 2000
E: Expected Count/Frequency	(500*835) / 2000	(500*740) / 2000	(500*230) / 2000	(500*195) / 2000

E: Expected Count/Frequency	Group Meetings	Face-to-Face Meetings with Individuals	E-mails	Other
Generation Y	208.75	185	57.5	48.7500
Generation X	208.75	185	57.5	48.7500
Boomer	208.7500	185	57.5000	48.7500
Mature	208.7500	185	57.5000	48.7500

O	E	O-E	(O-E)2	(O-E)2/E
180	208.75	-28.75	826.5625	3.9596
240	185	55	3025	16.3514
50	57.5	-7.5	56.25	0.9783
30	48.75	-18.75	351.5625	7.2115
230	208.75	21.25	451.5625	2.1632
165	185	-20	400	2.1622
50	57.5	-7.5	56.25	0.9783
55	48.75	6.25	39.0625	0.8013
220	208.75	11.25	126.5625	0.6063
185	185	0	0	0.0000
60	57.5	2.5	6.25	0.1087
35	48.75	-13.75	189.0625	3.8782
205	208.75	-3.75	14.0625	0.0674
150	185	-35	1225	6.6216
70	57.5	12.5	156.25	2.7174
75	48.75	26.25	689.0625	14.1346
			Total	62.7398

Value of the test statistic = 62.7398

Degrees of freedom = (Number of rows -1)x(Number of columns -1)=(4-1)x(4-1)=9

For 9 degrees of freedom,

p-value = 0.0000

As p-value < 0.10:level of significance ; Reject the null hypothesis.

There is sufficient evidence to conclude that There is relationship between age group and type of communication​ preferred(Age group and type of communication are not independent)