Statistic Exercises

Question 1
Stdev
VAR
Period

14%
0.0196
12

a) Check whether it can be asserted with 98% confidence that the underlying yearly real variance of the portfol
Sigma^2=
440
Ho: sigma^2 = 440
H1: sigma^2 not = 440

Statistic

4.9

With 98% confidence
Lower limit 3.05348411
Upper limit 24.7249703
With 98% confidence we cannot reject Ho since the statistic is inside the acceptance zone
b) Check the same hypothesis with 95% confidence. With 95% confidence
Lower limit 3.81574825
Upper limit 21.9200493
With 95% confidence we cannot reject Ho since the statistic is inside the acceptance zone
Question 2
Typical variance
Number of students
New variance
Normal population

300
30
480

a) Check whether the hypothesis that the population variance of their scores is 300 can be accepted with 95 % Ho: sigma^2 = 300
H1: sigma^2 not = 300

Statistic
46.4

Lower limit 16.0470717
Upper limit 45.7222858
We can reject Ho with 95% confidence since it falls outside of the interval

b) Check with 90% confidence the hypothesis that the population variance of the scores is greater or equal than
Ho: sigma^2 >= 300
H1: sigma^2<300

Limit

19.7677436

With 90% we cannot reject Ho since statistic (46.4) is higher than limit.

Question 3
Variance_1
114.09 during 4 years
Variance_2
16.08 following 7 years
Normal distribution
a) Test whether the two population variances can be considered equal with 95 % confidence.
Ho: sigma1^2 = sigma2^2
H1: sigma1^1 not equal to