Question

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 n=30 books and records the publication date for each. The sample produces an average age of M=23.8 years with a variance of s^2 = 67.5. Use this sample to conduct a one-tailed test with a=.01 to determine whether the average age of the library books in significantly greater than 20 years.  

Hypothesis Testing (Complete the 4 steps below)

Step 1: State the hypothesis and set the alpha level

Step 2: Locate the critical region

Step 3: Compute the test statistic for the sample

Step 4: Make a decision and state your conclusion about H0 based on the result of step 3

Step 5: Compute and interpret r^2

Answer 1

Step 1: State the hypothesis and set the alpha level

H₀: µ = 20 versus H_a: µ > 20

α = 0.01

Step 2: Locate the critical region

We are given

n = 30

df = n – 1 = 29

Critical t value = 2.4620

Critical region = t < 2.4620

Step 3: Compute the test statistic for the sample

Given

Xbar = 23.8

S² = 67.5

S = sqrt(67.5) = 8.215838363

t = (Xbar - µ)/[S/sqrt(n)]

t = (23.8 – 20) / [8.215838363/sqrt(30)]

t = 2.5333

Step 4: Make a decision and state your conclusion about H0 based on the result of step 3

P-value = 0.0085

(by using t-table)

α = 0.01

P-value < α = 0.01

So, we reject the null hypothesis

There is sufficient evidence to conclude that the average age of the library books in significantly greater than 20 years.