Degree of freedom For the accompanying screen display a simp

Degree of freedom. For the accompanying screen display, a simple random sample of size n=40 was obtained from the population of duration times (seconds) of eruptions of the Old Faithful geyser.

What is the number of degrees of freedom that should be used for finding th critical value t@/2?

Find the critical value t@/2 corresponding to n=40 and a 95% confidence level.

Give a brief general description of the number of degrees of freedom.

Solution

sample size,n = 40
number of degrees of freedom that should be used for finding the critical value ta/2 = n-1
= 39

a = 1-0.95 = 0.0540

critical value = t(a/2,n-1) = t(0.025, 39)
= 2.023

as degree of freedom increases t-distribution approaches normal distribution