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 #11.1.6 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? Test at the 1% level.

Table #11.1.6: Dolphin Activity

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

Answer 1

The hypothesis being tested is:

H₀: Activity and the time period are independent

H_a: Activity and the time period are not independent

		Morning	Noon	Afternoon	Evening	Total
Travel	Observed	6	6	14	13	39
	Expected	14.86	3.10	4.75	16.30	39.00
	O - E	-8.86	2.90	9.25	-3.30	0.00
	(O - E)² / E	5.28	2.73	18.04	0.67	26.72
Feed	Observed	28	4	0	56	88
	Expected	33.52	6.98	10.71	36.78	88.00
	O - E	-5.52	-2.98	-10.71	19.22	0.00
	(O - E)² / E	0.91	1.28	10.71	10.04	22.93
Social	Observed	38	5	9	10	62
	Expected	23.62	4.92	7.54	25.92	62.00
	O - E	14.38	0.08	1.46	-15.92	0.00
	(O - E)² / E	8.76	0.00	0.28	9.77	18.81
Total	Observed	72	15	23	79	189
	Expected	72.00	15.00	23.00	79.00	189.00
	O - E	0.00	0.00	0.00	0.00	0.00
	(O - E)² / E	14.95	4.00	29.03	20.48	68.46
		68.46	chi-square
		6	df
		8.44E-13	p-value

Since the p-value (0.0000) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we cannot conclude that the activity and the time period are independent for dolphins.