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guajiro [1.7K]
3 years ago
12

The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To te

st 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.
Mathematics
1 answer:
Cerrena [4.2K]3 years ago
3 0

Answer:

<em>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.</em>

Step-by-step explanation:

<em>Step 1: Hypotheses and α level </em>

H0: μ ≤ 20

H1: μ > 20

<u><em>α = 0.01</em></u>

<em>Step 2: Critical region </em>

α = .01

One-tailed

df = n – 1 = 30 – 1 = 29

<u><em>t - critical = 2.462 </em></u>

<em>Step 3: Calculate t which is observed </em>

sM = √(s2 / n) = √(67.5 / 30) = 1.5

t = (M – μ) / sM  

t = (23.8 – 20) / 1.5

<u><em>t = 2.533 </em></u>

<u><em /></u>

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