# finding the test statistic, p-value..

• Jun 17th 2009, 07:20 PM
tennisair
finding the test statistic, p-value..
Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, p-value, critical value(s), and state the final conclusion.
Test the claim that the mean age of the skating population in one city is less than 26 years. Sample data are summarized as n=25, x bar= 24.4 years, and s=9.2 years. Use significance level of 0.05
• Jun 17th 2009, 08:44 PM
matheagle
The test stat is

${\bar X-\mu_0\over s /\sqrt n} ={24.4-26\over 9.2 /5}$

NOW, some may use a z table, but this is really a t with 24 degrees of feedom.

So since, $H_a:\mu<26$ is my alternative hypothesis, my p-value is

$P\bigg(t_{24}< {24.4-26\over 9.2 /5}\biggr)$

which you can look up at....http://www.danielsoper.com/statcalc/calc08.aspx