MATH SOLVE

5 months ago

Q:
# 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.

Accepted Solution

A:

Answer: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 = 0.01Step 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