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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

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 s2 = 67.5. Use this sample to conduct a one-tailed test with α = .01 to determine whether the average age of the library books is significantly greater than 20 years ( μ > 20).

To determine

To state: The decision of hypothesis test performed for the given question using one-tailed test.

Explanation

Given info:

The data has the sample size of 30 with population mean, sample mean, and variance is 20, 23.8 and 67.5.

Calculations:

The test hypotheses are:

Null Hypothesis is H0:μ20

Alternate Hypothesis is H1:μ>20

Degrees of Freedom:

df=n1=301=29

The critical value is obtained from the t-table for tα=0.01(29)=1.699. So, CV=1.699

The estimated standard error, sm:

sm=sn=67.530=1

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