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

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.