Question

(1 point) 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 22 feet; however, one marine biologist believes that great white sharks off the Bermuda coast grow much longer. To test this claim, full-grown white sharks were captured, measured, and then set free. However, this was a difficult, costly and very dangerous task, so only four sharks were actually sampled. Their lengths were 25, 26, 26, and 22 feet. Do the data provide sufficient evidence to support the claim? Use a = 0.05. Round off your answers to three decimal places. (a) Calculate the test statistic: t = (b) Find the critical value: t* = (c) The final conclusion is A. We can reject the null hypothesis that the average length of the shark is 22. B. There is not sufficient evidence to reject the null hypothesis that the average length of the shark is 22.

Answer 1

24.750	mean Data
1.893	std. dev.

To Test :-

H0 :- µ = 22
H1 :- µ > 22

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = 2.91

Critical value t(α, n-1) = t(0.05 , 4-1) = 2.353

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 4-1) = 2.353
t > t(α, n-1) = 2.91 > 2.353
Result :- Fail to reject null hypothesis

Option B is correct