The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a sample of 30 books and records the publication date for each. The sample produces an average age of 23.8 years with a variance of 67.5. What test should you use to determine whether the average age of the library books is significantly greater than 20 years.

The observed t (2.533) is in the tail cut off by the critical t (2.462), therefore we reject H0. It is likely that the books are older than 20 years of age on average.

Step-by-step explanation:

Step 1: Hypotheses and α level

H0: μ ≤ 20

H1: μ > 20

α = 0.01

Step 2: Critical region

α = .01

One-tailed

df = n – 1 = 30 – 1 = 29

t - critical = 2.462

Step 3: Calculate t which is observed

sM = √(s2 / n) = √(67.5 / 30) = 1.5

t = (M – μ) / sM

t = (23.8 – 20) / 1.5

t = 2.533