Question

Degrees of Freedom In general, what does “degrees of freedom” refer to? For the sample data described in Exercise 7 “Requirements,” find the number of degrees of freedom, assuming that you want to construct a confidence interval estimate of \(\mu \)using the t distribution.

Short answer

The degrees of freedom refer to the number of values that can be considered independent while estimating a population parameter.

The value of the degrees of freedom to estimate the mean voltage level of smartphone batteries is equal to 11.

Step-by-step solution

Given information

Referring to Exercise 7 CQQ, it is given that a sample of size 12 is selected,showing the voltage level of smartphone batteries.

Degrees of freedom

The number of values that can be considered independent in estimating a population parameter is called the degrees of freedom.

In other words, it is the value obtained by subtracting those number of parameters from the total number of values available thatare used in the intermediate steps to compute the sample statistic.

Here, to construct the confidence interval of the mean value using the t distribution, the mean used to compute the interval is calculated from the sample values.

Thus, the sample mean (the parameter used inbetween the steps) is to be used to compute the confidence interval and is calculated from the available data.

Therefore, the degrees of freedom areas follows:

\(\begin{array}{c}df = {\rm{Total}}\;{\rm{number}}\;{\rm{of}}\;{\rm{values}} - {\rm{Number}}\;{\rm{of}}\;{\rm{parameters}}\\ = n - 1\\ = 12 - 1\\ = 11\end{array}\)

Thus, the value of the degrees of freedom is equal to 11.