Question

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities...

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

Homework Answers

Answer #1

The hypothesis being tested is:

H0: Activity and the time period are independent

Ha: 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.

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