Question

Does the lifespan of a shark depend on the species of shark? It is known that the lifespan depends on whether the shark is begin held in captivity or in the wild. For consistency, a researcher used GPS to track several sharks in the wild from four different species. Using the data provided , perform the appropriate test to determine if there is evidence that the average lifespan is different for at least one species of shark. Be sure to include all the necessary steps.
  

* * the commas separate the numbers between each shark. if there is a ,, that means to skip to the third shark.
Subject: Tiger Shark, Great White, Blue Shark, Hammerhead

1: 26, 31, 9, 23

2: 22,32, 12, 24

3: 31, 21, 20, 31

4: 24, 32, 21, 29

5: 36, 21, 16, 28

6: 29, 28, 19, 32

7: 30, 27, 11, 25

8: 26, 30, 21,

9: 27, , 16,

10: 23, ,22,

11: 29

12: 26

Answer 1

Would answer this using one way ANOVA

Here is the data:

Subject	Tiger Shark	Great White	Blue Shark	Hammerhead
1	26	31	9	23
2	22	32	12	24
3	31	21	20	31
4	24	32	21	29
5	36	21	16	28
6	29	28	19	32
7	30	27	11	25
8	26	30	21
9	27		16
10	23		22
11	29
12	26

The following table is obtained:

	Group 1	Group 2	Group 3	Group 4
	26	31	9	23
	22	32	12	24
	31	21	20	31
	24	32	21	29
	36	21	16	28
	29	28	19	32
	30	27	11	25
	26	30	21
	27		16
	23		22
	29
	26
Sum =	329	222	167	192
Average =	27.417	27.75	16.7	27.429
\sum_i X_{ij}^2 =∑i​Xij2​=	9185	6304	2985	5340
St. Dev. =	3.872	4.528	4.668	3.505
SS =	164.91666666667	143.5	196.1	73.714285714285
n =	12	8	10	7

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ₁ = μ₂ = μ₃ = μ₄

Ha: Not all means are equal

The above hypotheses will be tested using an F-ratio for a One-Way ANOVA.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df1​=3 and df2​=3, therefore, the rejection region for this F-test is R={F:F>Fc​=2.892}.

(3) Test Statistics

(4) Decision about the null hypothesis

Since it is observed that F=16.259>Fc​=2.892, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0, and since p=0<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that not all 4 population means are equal, at the α=0.05 significance level.

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