Question

you are performing a two - tailed t - test with test statistic ( t=-2.65 ) and a sample of size 30, find the p - value to 4 decimal places.

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 30\). So \(df=30-1 = 29\).

Step2: Use the t - distribution table or software

Since it is a two - tailed test, we find the probability \(P(T< - 2.65)+P(T>2.65)\). Using a t - distribution table or software (e.g., in R: 2pt(-2.65,29) or in Excel: =2T.DIST(-2.65,29,TRUE)).
When we calculate \(2\times P(T < - 2.65)\) with \(df = 29\), we get \(P(T< - 2.65)\approx0.0067\) (using t - distribution tables or software). Then \(2\times0.0067 = 0.0134\)

Answer:

\(0.0134\)