Question

A fish hatchery manager has two ponds containing largemouth bass, a predatory fish. The bass in Pond A were supplied with small fish (40-60 mm in length) to serve as a supplemental food source; the bass in Pond B were not. The manager would like you to determine if the supplemental feeding improved the growth rates of the bass. He graciously agreed to provide the following data taken from a random sample of fish from each pond.

Pond A (Fed) Total length (mm) Pond B (not fed) Total length (mm) 40 50 75 79 68 125 126 51 125 56 60 57 77 57 59 59 68 126 59 129 6 56 45 110 124 120 64 52 55 60 57 54 58 140 119 54,

Perform the appropriate tests to help this cooperative fellow determine whether feeding influenced growth rates.

Answer 1

POND A AND POND 2 ARE TWO INDEPENDENT SAMPLES.WE WILL CARRY OUT INDEPENDENT T TEST.

NULL HYPOTHESIS H0:

μ(A) = μ(Β)

ALTERNATIVE HYPOTHESIS Ha:

μ(Α) > μ(Β)

Level of significance =0.05

By using data analysis tool pack of EXCEL we have

t-Test: Two-Sample Assuming Unequal Variances PONDA 78.63333333 1127.205747 30 PONDB 67.36666667 105.0678161 Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 34 1.757933763 0.043879739 1.690924198 0.087759478 2.032244498

Test statistic t

t = ca – zb/ (san1 + sb/n2)

t = 78.63 – 67.37/(1127.21/30+ 105.07/30)

t = 1.758

Degrees of freedom= 34

P value=0.044

Since P value SMALLER than 0.05 therefore SIGNIFICANT

Decision: REJECT H0.

Conclusion: We have sufficient evidence to conclude that feeding influenced growth rates at 0.05 level of significance.