Statistical Analysis including all steps please eg hypothesi

Statistical Analysis [including all steps please, e.g. hypothesis, assumptions,conclusion... ]

Solution

Solution:

a)

Null Hypothesis: H₀ : u₁=u₂ , i.e the average number fat fish is same in both streams. Where u₁ and u₂ are averages of Upstream and Downstream.

Alternative Hypothesis: H₁ : u₁ ? u₂

Test Statistics: Under Ho the test-statistic is

                              t= (u₁ - u₂) / s*(1/n₁-1/n₂)^1/2

                              u₁=Average of Upstream

                              u₂₌ Average of Downstream

Computation:

                    

The tabulated value of t for 22 d.f at 5% level of significance for two tailed test is 2.07.

Conclusion: Since calulated \"t\" is less than tabulated \"t\", it is not significant. hence null hypothesis is accepted and we conclude that average number of fat fish is same.

b)   Power Analysis:

     When n=20     power of the test is 0.03

               n=30    power of the test is 0.04

               n=50    power of the test is 0.04

               n=80    power of the test is 0.05

	Upstream	Down stream
	14	19
	11	18
	8	8
	5	7
	10	16
	5	6
	23	24
	29	30
	19	16
	16	20
	25	21
	10	12
	175	197
	Upstream	Down stream
Mean	14.58333333	16.41666667
Variance	62.81060606	52.08333333
Observations	12	12
Hypothesized Mean Difference	0
df	22
t Stat	-0.5924