Question

The librarian at the local 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. The sample of 30 books produce an average age of M = 23.86 years with a standard deviation of 8.82 years. Conduct a one-tailed test with α = .01 to determine whether the average age of the library books is significantly greater than 20 years.

Show all your work. Full marks will not be given unless all steps and all calculations are shown. For all hypothesis tests, include all steps. Remember to provide concluding statements in the proper format.

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H₀ : = 20

H_a : > 20

Test statistic = t

= ( - ) / s / n

= (23.86 - 20) / 8.82 / 30

= 2.397

Test statistic = 2.397

df = 29

P-value = 0.0116

= 0.01

P-value >

Fail to reject the null hypothesis .

There is sufficient evidence to conclude that the average age of the library books

is significantly greater than 20 years.