Question

4. One of the most feared predators in the ocean is the great white shark. It is known that the white shark grows to a mean length of 21 feet; however, one marine biologist believes that great white sharks off the Bermuda coast grow much longer owing to unusual feeding habits. To test this claim, some fully-grown great white sharks were captured off the Bermuda coast, measured, and then set free. However, because the capture of sharks is difficult, costly, and very dangerous, only three specimens were sampled. Their lengths were

24,20,22

feet. Do the data provide sufficient evidence to support the marine biologist’s claim? Use α= 0.05. (15pts.)

Answer 1

Calculate Mean and sample Std dev :

Sample standard deviation s:

Hypothesis :

H₀:µ=21

H₁:µ >21

Test statistics :

Critical Value :

df=n-1=3-1=2 at 0.05 level of significance,

............Crtical value t table

Conclusion & Decision :

Rejection region =2.92 is greater than calculated test statistics value =0.8660

Then Fail to reject the null hypothesis

There is not sufficient evidence to support the marine biologist claim