Question

given degree of freedom df = 5, find the probability by using the students t distribution: p(t>0.2)= round your answer to three decimal places.

Explanation:

Step1: Use the t - distribution property

We know that for a t - distribution with degree of freedom \(df = n-1\) (here \(n = 6\) since \(df=5\)), and we want to find \(P(t>0.2)\). We can use a t - table or a statistical software. Using a t - table (right - tailed), for \(df = 5\).

Step2: Look up the value

Looking up the value in the t - table (right - tailed), when \(df = 5\), \(P(t>0.2)\). Using a calculator or software (e.g., in R: 1 - pt(0.2,5)), we calculate the probability.

$$P(t>0.2)=1 - P(t\leq0.2)$$

The cumulative distribution function of the t - distribution \(P(t\leq x)\) with \(df = 5\) and \(x = 0.2\). Using the formula or software, \(P(t\leq0.2)\approx0.576\) (from t - table or calculation). Then \(P(t>0.2)=1 - 0.576=0.424\)

Answer:

\(0.424\)