df If we are using the sample data from Exercise 1 for a t-test of the claim that the population mean is greater than 90sec, What does df denote, and what is its value?

Refer to Exercise 1 for the observations and claim.

84 14 583 50 0 57 207 43 178 0 2 57

The population mean is greater than\(\left( \mu \right)\)90 sec.

The total number of observations is 12 (n).

The claim is expressed as follows:

\(\begin{array}{l}{H_0}:\mu = 90\;({\rm{null}}\;{\rm{hypothesis}})\\{H_1}:\mu > 90\;({\rm{alternative}}\;{\rm{hypothesis}}\;{\rm{and}}\;{\rm{original}}\;{\rm{claim}})\end{array}\)

Here, \(\mu \)is the population mean of duration times.

The degrees of freedom (df) denote thenumber of independent observations in the data.

For the t-test, the degrees of freedom are given as follows:

\(\begin{array}{c}df = n - 1\\ = 12 - 1\\ = 11\end{array}\)

The value of the number of independent observations in the given data is 11.