Question

question 15
given degree of freedom df = 13, find the probability by using the students t distribution: p(t>2) =
round your answer to three decimal places.
question help: video message instructor

Explanation:

Step1: Use the t - distribution table or software

We can use a t - distribution table (one - tailed) with \(df = 13\) or a statistical software (such as R: 1 - pt(2, 13) or Python with scipy.stats.t.sf(2, 13)).
Using the formula for the survival function of the t - distribution \(P(t>x)=1 - F(x)\) where \(F(x)\) is the cumulative distribution function of the t - distribution.

Step2: Calculate the probability

Using a t - table (one - tailed), for \(df = 13\), the value of \(P(t>1.771)=0.05\) and \(P(t>2.160)=0.025\).
Using software:
In R:

1 - pt(2, 13)

The result is approximately \(0.033\).
In Python:

from scipy.stats import t
print(1 - t.cdf(2, 13))

The result is also approximately \(0.033\).

Answer:

\(0.033\)