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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 |
|||
|
Morning |
Noon |
Afternoon |
Evening |
||
|
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:
Ha: 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 |
|
|
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 |
|
|
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 |
|
|
7.139123 |
0.041839 |
0.02035 |
5.952506 |
13.15382 |
|
Column Total |
72 |
19 |
25 |
85 |
201 |
|
Expected |
72 |
19 |
25 |
85 |
201 |
|
|
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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