MBS
8.37 (20 points)
n=200 x=17.05 
=5.21
a)
H
: 
H
: 
b)
Z-stat=
=1.493
p-value=1-P(1.493<=Z-stat)=0.0681
c)
In this case, out
alternative hypothesis is to “greater than”, not “ not equal to”.
So, we only need to test
the right side error, the right-tail test is more appropriate.
8.99 (20 points)
a) H
: 
H
: 
b)
Z-stat=
=1.86
If
we pick 
, Z
=1.645, We reject the null hypothesis.
d)
In this context, the
statistical significance level is 
. The practical significance is the
p-value, which is 0.0314.
9.16 (30 points)
Chatterjee Case Book Question (30 points)
1)
Two Sample T-Test and Confidence Interval
Two sample T for Fixed vs
Adjustable
N Mean StDev
SE Mean
Fixed 14
7.357 0.404 0.11
Adjustab 6
4.917 0.645 0.26
95% CI for mu Fixed - mu
Adjustab: ( 1.74, 3.14)
T-Test mu Fixed = mu
Adjustab (vs not =): T = 8.57 P =
0.0001 DF = 6
Apparently, we should reject
the null hypothesis.
2)
For the Saracco
study:
|
Sample |
Infected Couples |
Total Couples |
Estimated P |
|
Without using
Condom |
8 |
55 |
0.145455 |
|
Using condom |
3 |
171 |
0.017544 |
Z-stat=2.63 P-value=0.008
The tail probability is the
p-value.
For European studies:
|
Sample |
Infected Couples |
Total Couples |
Estimated P |
|
Without using
Condom |
12 |
122 |
0.098361 |
|
Using condom |
0 |
123 |
0.000000 |
z-stat=3.65 p-value=0.0002
P-value is just twice as big
as the tail probability. It is easy to understand. The tail
Probability is the
probability of the two tails, while the p-vale is only the right hand
Side tail probability.