Number of Degrees of Freedom

1.
2. For each of the following statements, circle the letter “T” if it is true, and “F” if it is false.
(2 *9 = 18)
T F (a) The number of degrees of freedom in the numerator of the f statistic is n1-1 when
testing σ1 vs. σ2.
T
T F (b) In regre ssion anal ysi s, the term Sxx quantifie s the scatter of x about 𝑥𝑥̅ .
F
T F (c) Zα < Tα, v for all cases α<0.5 when v < 40.
T
T F (d) The standard error for the population proportion derived from sample data is
p(1-p)/n
F
T F (e) Since the definition of population 1 and 2 are interchangeable when conducting
hypothesis testing on the variance, fα,u,v = fα,v,u for all α, u, v.
F
T F (f) 2α1,v > 2α2,v for all values of α1<0.5 and α2<0.5 as long as α1 > α2.
F
T F (g) √ s2
n is the standard error of the sample variance.
T
T F (h) The p-value defines the acceptance region of a hypothesis test.
T
T F (i) Linear least squares regression analysis assumes that the independent variable x and
the dependent variable y are normally distributed.
T
1. (20 pts) A researcher claims that more than 10% of football helmets have manufacturing
flaws that could potentially cause injury to the wearer. A sample of 85 helmets revealed
that 9 helmets contained such defects.
(a) (5 pts) Perform a hypothesis test to determine if the data supports the researchers
claim. Use α = 0.05.
p0=0.1
p= 9
85 =0.1059
H0 : p= p0
H1 : p> p0