1. (Degrees of Freedom) You want to determine the mean height of fourth-graders in Massachusetts.You will...
1. (Degrees of Freedom) You want to determine the mean height of fourth-graders in Massachusetts.You will do this by randomly choosing 40 fourth-graders from around the state.
(a) You calculate the sample mean for these fourth graders. How many degrees of freedom doesthis estimator have?
(b) You calculate the sample variance for these fourth graders. How many degrees of freedom doesthis estimator have?
(c) You calculate the sample standard deviation for these fourth graders. How many degrees offreedom does this estimator have?
(d) One year later, you determine the heights of the same 40 students as fifth-graders. Youdetermine the sample correlation coefficient between the students’ heights as fourth gradersand as fifth graders. How many degrees of freedom does this estimator have?Explain youranswer.(Hint: To calculate the correlation coefficient by hand, you have to calculate themean and variance of each group.
Homework Answers
Degrees of Freedom: It is defined as the total number of observations minus the number of independent constraints imposed on the observations.
a) Here n = 40 (Test for mean) (t or z test)
d.f = (n-1) = (40-1) = 39
b) Test for variance: (chi-square test)
d.f = (n-1) = (40-1) = 39
c) Test for standard deviation (chi-square test)
d.f = (n-1) = (40-1) = 39
d) Test for correlation ( t test)
d.f. = (n-2) = (40-2) = 38
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