Question

Problem 3 The historical mean width of the Atlantic littleneck clam is 4.75 cm. Following a recent spill off the coast of Maine, a biologist was concerned that the mean width of littleneck clam could have decreased.

(a) Formulate the null and the alternative hypotheses to test the biologist’s concern.

(b) A random sample of 26 littlenecks was obtained and the width of each was recorded. The summary statistics were ?̅ = 4.66 ?? and ? = 0.25 ??. Assume that the width of littleneck clams is normally distributed. Calculate the value of the test statistic for the hypotheses in (a), state the degrees of freedom, and approximate the p-value

. (c) Would you reject H0 or fail to reject H0 at 5% level of significance?

(d) What would you conclude about the mean width of little neck clams after the spill?

Answer 1

a)

H0: = 4.75 , Ha: < 4.75

b)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 4.66 - 4.75 ) / ( 0.25 / √(26) )
t = -1.84

c)

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 26-1) = 1.708
t < - t(α, n-1) = -1.8356 < - 1.708
Reject null hypothesis

d)

Conclusion = We have sufficient evidence to support the claim that the mean width of littleneck

clam could have decreased.