Question

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?

Short answer

The degrees of freedom of the data denote the number of independent observations in it. The value is 11.

Step-by-step solution

Given information

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 90 sec.

The total number of observations is 12 (n).

State the hypotheses

The claim is expressed as follows:

$$\begin{gathered} H_0:\mu =90(\text{null}\text{hypothesis}) \\ {H}_1:\mu >90(\text{alternative}\text{hypothesis}\text{and}\text{original}\text{claim}) \end{gathered}$$

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

Compute the degrees of freedom

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

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

$$\begin{gathered} df=n-1 \\ =12-1 \\ =11 \end{gathered}$$

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