Lia Liu
Stat 101 Review for Final Spring 2013
1
Lia Liu
The final exam is on Thursday, 10:30-12:30pm. Room assignment will be posted later. You can bring two sheets of formula
and calculator. Final covers Chapter 18-23 only, is worth 200
points. Use the following check list of concepts and the Practice
for Final on your MyLab to prepare for the final.
List of topics:
1. Sampling distribution: If X1 , X2 , , Xn is a random sample
from a population with mean µ and standard deviation σ,
n
has mean E(X̄) = µ,
then the sample mean X̄ = X1 +...+X
n
variance V (X̄) = σ 2 /n.
The sample sum Sn = X1 + ... + Xn has mean E(Sn ) = nµ, and
variance V (Sn ) = nσ 2 .
What about 2X1 −3X2 ? Can you find the mean and variance?
If X has binomial B(n, p), what are the mean and variance
of X? what are the mean and variance of p̂ = Xn ? How to
use normal to approximate probability? What conditions
must be checked?
2. How to standardize a random variable X(find the z-score)?
Subtract by the mean of X, then divide by the standard
deviation of X.
3. Fundamental theorem of statistics (Central Limit Theorem): Apply to X̄, apply to p̂.
4. Use Empirical rule to describe a distribution, or estimate
probability or decide whether an event is unusual. (See
textbook Page 480: 13,16,18,19,22.)
5. Confidence interval: estimate ± margin of error
6. How wide is a confidence interval?
7. How can you cut the width of a confidence interval by half
but keep the same confidence level?
Lia Liu
8. Confidence interval for p (Binomial model): p̂ ± z
large enough.(When is n large enough?)
2
∗
r
p̂q̂
n
if n is
9. Confidence interval for p1 − p2 (2 Binomial proportions):
(p̂1 − p̂2 ) ± z ∗ × SE(p̂1 − p̂2 ) , if n1 , n2 are large enough.(When
are they large enough?)
10. Confidence interval for µ (Normal model): (1) x̄ ± z ∗ √σn if
the standard deviation for the population, σ, is given;
(2) x̄ ± z ∗ √sn if the standard deviation for the population, σ,
is not given but n is large;
(3) x̄ ± t∗(n−1) √sn if the standard deviation for the population,
σ, is not given and n is small.
11. Hypothesis testing for p, µ, p1 − p2 : 1)know how to read a
story and write down the hypotheses. 2) which conditions
to check; 3) find P-value; 4) give conclusion, and interpret
your conclusion.
12. For inferences of p1 − p2 , which standard error do we use
to approximate standard deviation of p̂1 − p̂2 in hypothesis
testing? Which one do we use in confidence interval for
p1 − p2 ? Why?
13. How to find p-values?
14. How to make a decision based on the p-value?
15. What is a Type I error?
16. What is a Type II error?
17. What is the power of a test?
18. Can you reduce both Type I and Type II error at the same
time?