Standard deviation standard error n p p 1 n p p p p z

standard deviation (standard error)
n
p p ) 1 ( 

n
p p
p p
Z
) 1 ( 


Parameter Situation
Confidence
Interval for
Parameter
Comment

 σ known
 X normally
distributed or n ≥ 30
n
z x


For z use the value z* such that
P(-z* < Z < z*) = confidence coefficient
.
It
is rare to know  when you don’t know  .

  unknown
 X normally distrib-
uted or n  30 n
s
t x 
Reference the t-distribution with n-1
degrees of freedom. For t use the value
t* such that
P(-t* < t < t*) = confidence
coefficient
.
n
s
is an estimate of
n

.
p
 np  5 and n(1-p)  5
(i.e.,
n
p
n
5
1
5
  
)
n
p p
z p
) 1 ( 

For z use the value z* such that
P(-z* < Z < z*) = confidence coefficient
.
n
p p ) 1 ( 
is an estimate of
n
p p ) 1 ( 
.
Parameter for
which confidence
interval sought
Sample size to achieve pre-set
confidence level and margin of error
(E) targets
Comment


2
2 2
) (
E
of estimate z
n


If calculated n is < 30, actually
sample 30. If X is estimated to
range from L to H, may use
4
L H 
as estimate of σ.
p
2
2 ) 1 )( (
E
p of estimate p of estimate z
n


If no estimate of p is available,
substitute .50 for estimate of p .
Practice Problems for Test #3
 For all hypothesis testing problems, use the p-value approach.
Chapter 9 Hypothesis Testing
8. Out of a random sample of 150 employees of a large company, 22 indicated that they
planned to take an early retirement. Does this sample suggest that more than 10% of all the
company's employees plan to take an early retirement? Would a person desiring to use a
significance level of .01 reject the null hypothesis?
Chapter 11 Chi-Square Test of Independence
9. A financial consultant wishes to determine whether, for firms in a given industry, there is a
relationship between firm asset size and capital structure. A random sample of 134 firms in
the industry was selected, and cross-classified as follows:
firm asset size
capital structure low medium high
debt less than or = equity 14 20 16
debt greater than equity 30 36 18
Does this sample data provide evidence to conclude that firm asset size and capital
structure are related?
Chapter 9 Hypothesis Testing
10. A mail order company’s standard shipping fee is based on the assumption of a mean package
weight of 20 ounces. A random sample of 40 packages sent out recently had a mean weight of
21.3 ounces with a standard deviation of 3.7 ounces. Does this sample suggest that the mean
weight of the packages sent out by this company is not 20 ounces? Would a person desiring to
use a significance level of .10 reject the null hypothesis?
Chapter 3 Correlation Coefficient