You know the population mean for a certain test score. You select 10 people from the population to estimate the standard deviation. How many degrees of freedom does your estimation of the standard deviation have?
There are 10 independent pieces of information, so there are 10 degrees of freedom.
10
0.0
You do not know the population mean for a different test score. You select 15 people from the population and use this sample to estimate the mean and standard deviation. How many degrees of freedom does your estimation of the standard deviation have?
The degrees of freedom for an estimate is equal to the number of values minus the number of parameters estimated en route to the estimate in question. You have 15 values in your sample, and you need to estimate one parameter, the mean, in order to find the standard deviation. 15 - 1 = 14.
14
0.0
For which of these degrees of freedom do you think your sample statistic is the least likely to be an accurate representation of the popoulation parameter?
false
21
false
5
true
2
false
100
2 degrees of freedom gives the least information. It had the smallest sample used to compute the statistic and is therefore the most likely to be a poor representation of the population parameter.