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.