Question

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013). The numbers in Table 3 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Is there enough evidence to show that the activity and the time period are independent for dolphins? Why or Why not? Test at the 1% level.

Activity	Morning	Noon	Afternoon	Evening	Row Total
Travel	6	6	14	13	39
Feed	28	4	0	56	88
Social	38	5	9	10	62
Column Total	72	15	23	79	189

Answer 1

Ans:

H₀:the activity and the time period are independent for dolphins.

H_a:the activity and the time period are dependent for dolphins.

Observed(fo)
Activity	Morning	Noon	Afternoon	Evening	Row Total
Travel	6	6	14	13	39
Feed	28	4	0	56	88
Social	38	5	9	10	62
Column Total	72	15	23	79	189
Expected(fe)
Activity	Morning	Noon	Afternoon	Evening	Row Total
Travel	14.86	3.10	4.75	16.30	39
Feed	33.52	6.98	10.71	36.78	88
Social	23.62	4.92	7.54	25.92	62
Column Total	72	15	23	79	189
Chi square=(fo-fe)^2/fe
Activity	Morning	Noon	Afternoon	Evening	Row Total
Travel	5.28	2.73	18.04	0.67	26.72
Feed	0.91	1.28	10.71	10.04	22.93
Social	8.76	0.00	0.28	9.77	18.81
Column Total	14.95	4.00	29.03	20.48	68.46

Test statistic:

Chi square=68.46

df=(3-1)*(4-1)=6

alpha=0.01

critical chi square value=CHIINV(0.01,6)=16.812

As,test statistic chi square is greater than critical chi square value,so reject the null hypothesis.

There is not enough evidence to conclude that the activity and the time period are independent for dolphins.