Small Sample Mean Problem. Each year the Heritage Foundation creates an Index of

Question

Small Sample Mean Problem. Each year the Heritage Foundation creates an Index of Economic Freedom for countries around the word based on assessments of freedom on property rights, corruption, business freedom, and labor freedom, among many others. We have a sample of 31 countries taken from the 2016 data.   The following is a summary of this sample.

The Heritage Foundation feels an index below 60 reflects a country that is mostly unfree. If we were to conduct a test to see if the sample estimate is above 60 at an alpha level = .10, what is the test statistic for this test?

Explanation / Answer

Solution

Let xbar be the mean of the indexes of the 31 countries. And s be the sample standard deviation. Then, the test statistic for testing if the sample estimate is above 60 at an alpha level = .10 is:

t = (?31)(xbar - 60)/s. This has t-distribution with 30 degrees of freedom (i.e., n - 1).

Being a one-sided (right tail, i.e, greater than type alternative), the null hypothesis will be rejected if the calculated value of t is greater than 1.31 (the upper 10% point oft-distribution with 30 degrees of freedom.)

DONE

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.