Question

An oceanographer wants to test, on the basis of the mean of a random sample of size ? = 35 and at the 0.05 level of significance, whether the average depth ocean in a certain area is 72.4 fathoms, as has been recorded. What will she decide if she gets ?̅ = 73.2 fathoms, and she can assume from information gathered in similar studies that σ = 2.1 fathoms?

Answer 1

Solution:

Z = (X – µ)/(σ/√n)

Z = (73.2–72.4)/ (2.1/√35)

Z = 0.8/0.354964787

Z = 2.253744679

Z = 2.2537 (rounded)

=> For significance level of 0.05, Z is greater than or equal to 1.64, hence the null hypothesis should be rejected. The value is 2.3 fathoms, which is greater than the population mean of 2.1 fathoms.