| Tag | Value |
|---|---|
| file | Inferential_Statistics_uu-t-test-800-en_uu-t-test-800-en |
| name | uu-t-test-800-en.Rmd |
| section | Inferential Statistics/Parametric Techniques/t-test |
| type | string |
| solution | "Step 1 Hypotheses |
| Type | Case |
| Language | English |
| Level | Statistical Literacy |
An employee at the local library claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a random sample of 30 books and records the publication date for each. In this sample the mean age of the books is 23.8 years and the variance (s2) is 67.5.
Use the five steps of hypothesis testing to answer the research question:
Are the books in the library, on average, more than 20 years old?
Use the .01 level of significance.
Step 1 Hypotheses Hr: μ = 20 H0: μ >20 (0.5 points)
Step 2 Comparison Distribution Sm = √67.5/30 = 1.5 (0.5 points)
Step 3 Cutoff α =.01; one-tailed tcritical = 2.462 (0.5 points)
Step 4 sample’s score t = 23.8-20/1.5 = 2.53 (0.5 points)
Step 5 Reject? 2.53>2.462, so reject H0. This means that in the population, on average, the books are probably more than 20 years old. (1 point)