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Stat-200 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.

Stat-200 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.: Expert Solutions for Success

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. The numbers in table C 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 5% level. Hint: Start by calculating the row and column totals.

Table C: Dolphin Activity

Activity	Period				Row Total
Activity	Morning	Noon	Afternoon	Evening	Row Total
Travel	6	7	14	13
Feed	28	6	2	56
Social	38	6	9	16
Column Total

Answer

The Hypotheses are stated below:

Null hypothesis:

H₀: The activity for the dolphins is not independent of the time period.

Alternative hypothesis:

H_a: The activity for the dolphins is independent of the time period.

From the given information, the significance level taken as the 5%, that is 0.05 is the level of the significance of this test.

Activity	Morning	Noon	Afternoon	Evening	Row Total
Travel	6	7	14	13	40
Expected	14.32836	3.781095	4.975124	16.91542	40
x²	4.840858	2.740305	16.37112	0.906305	24.85859
Feed	28	6	2	56	92
Expected	32.95522	8.696517	11.44279	38.90547	92
x²	0.745079	0.836106	7.792351	7.511099	16.88463
Social	38	6	9	16	69
Expected	24.71642	6.522388	8.58209	29.1791	69
x²	7.139123	0.041839	0.02035	5.952506	13.15382
Column Total	72	19	25	85	201
Expected	72	19	25	85	201
x²	12.72506	3.618249	24.18383	14.36991	54.89705

The chi-square for this data is thus 54.89705 and the p-value from the chi-square table is 0.0000. Since the p-value is less than alpha value; that is 0.0000 < 0.05, there is sufficient evidence to reject the null hypothesis and conclude that the activity for the dolphins is independent of the time period.

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