MATH 1070-070: Final Exam
June 17, 2008
Name:
No outside materials are allowed except pens, pencils, erasers, and calculators. You have one
half hour to complete this quiz. Please keep nervous ticks to a minimal so as to not disrupt
anyone else taking the quiz. Anyone caught cheating will be punished with a grade of 0%.
You may need the following:
n
n
i=1
i=1
1X
1 X
x̄ =
Xi , SX =
(xi − x̄)2
n
n−1
IQR = Q3 − Q1 , Q1 − 1.5(IQR), Q3 + 1.5(IQR)
68% in x̄ ± Sx , 95% in x̄ ± 2Sx , All in x̄ ± 3Sx
r=
1 X x − x̄
1 X
y − ȳ
Zx Zy =
n−1
n−1
Sx
Sy
Sy
, a = ȳ − bx̄
ŷ = a + bx, b = r
Sx
µ=
n
X
xi P (xi )
i=1
P (Ac ) = 1 − P (A), P (A or B) = P (A) + P (B) − P (A and B),
For X, a normal random variable:
z=
√
x−µ
x̄ − µ
, estimate of µ = x̄, µx̄ = µ, s.e.x̄ = σ/ n, x̄ ± t(s.e.), d.f. = n − 1, zx̄ = √
σ
s/ n
For X, a binomial random variable:
r
p
n!
p(1 − p)
P (x) =
px (1 − p)n−x , µx = np, σx = np(1 − p), µp = p, s.e.p =
,
x!(n − x)!
n
r
p
p̂ − p0
p0 (1 − p0 )
estimate of p = p̂, sep̂ = p̂(1 − p̂)/n, p̂ ± z(se), z =
, where s.e. =
s.e.
n
1