Download Study Guide for Exam 2 - Winona State University

Study Guide for Exam 2 ~ STAT 210
Chapter 8 & 11 ~ Normal Distribution and Central Limit Theorems
(Note: Book refers to these as
The Law of Averages)
 Given X ~ N(  ,  2 ) be able to find probabilities and quantiles
associated with X.
Practice Problems: 8.11, 8.13
 Normal approximation to the Binomial Distribution.
Practice Problems: 8.29, 8.43, 8.49
K ~ N (n , n (1   ) ) provided n is sufficiently large ( n  5 & n(1   )  5 ).
 Know what the central limit theorem for the sample proportion says
and how to apply it.
Practice Problem: 11.37

 (1   ) 
P ~ N   ,
 provided n is sufficiently large ( n  5 & n(1   )  5 ).
n


 Know what the central limit theorem for the SUM says and how to
apply it.
Practice Problems: 11.40, 11.41, 11.43
SUM ~ N (n , n ) provided X is normal to begin with or n is “large” (n  40) .

Know what the central limit theorem for the sample means says and
how to apply it.
Practice Problems: 12.5
  
X ~ N   ,
 provided X is normal to begin with or n is “large” (n  40) .
n

1
Chapter 12 – z and t Tests of Hypotheses
 Be able to conduct a z-test “by hand”. Specifically be able to set up
the hypotheses to be tested, compute the test statistic, find the
associated p-value and state your conclusions correctly using both in
statistical and non-statistical terms.
Practice Problems: 12.5, 12.17
 Be able to answer the question: “What the hell is a p-value anyway?”
 Be able to interpret output from a t-test conducted in JMP and
interpret output from the t-Probability calculator. This includes being
able to read a normal quantile plot.
Chapter 13 – Estimation with Confidence (Confidence Intervals)
 Be able to construct and interpret a 100(1-2)% CI for a population
mean (  ) using the t-table in your text to find the appropriate
t-quantile, e.g. t.975 .
x  t
s
n
  x  t 2
  x  t 2
(two-sided)
s
n
s
n
(one-sided upper)
(one-sided lower)
Practice Problems:
13.11, 13.13, 13.15 (a.) x  924.8, s  136.6) , 13.41,
13.51. 13.53
 Be able to construct and interpret a 100(1-2)% CI for a population
proportion (  ). You only need to know the large sample case:
p(1  p)
(two-sided)
n
p(1  p)
(one-sided upper)
  p  z 2
n
p(1  p)
(one-sided lower)
  p  z 2
n
p  z
Practice Problems: 13.29, 13.49
2
 Given an estimate of  you should be able to determine the sample
size needed to have a given margin of error when estimating the mean
with a 100(1-2)% CI. (see pages 367-368)
z  
Required sample size n   1 
 E 
2
Practice Problems: 13.19, 13.21
 You should be able to determine the sample size needed to have a
given margin of error when estimating the population proportion with
a 100(1-2)% CI. (see pages 371-372)
z 
Required sample size n   1 
 2E 
2
(conservative)
2
z 
Required sample size n   1   (1   ) (prior knowledge for )
 E 
Practice Problem: 13.27
3