Question

Use KS test to see if it conforms to a Beta distribution with
**shape1=4**, **shape2=7**. What is the
p-value?

0.18573722 0.41073334 0.56355831 0.06673358 0.43762574 0.45158744 0.27369696

0.27787527 0.27522373 0.22834730 0.28829185 0.21342879 0.24438748 0.37434856

0.53836814 0.34561632 0.28320219 0.22540641 0.23575321 0.38607398 0.28625720

0.29384326 0.44312820 0.25625404 0.15563416 0.46424265 0.21000100 0.36114007

0.22198265 0.56719777

Answer #1

For the data below, use Anderson-Darling test to see if it
conforms to a Beta distribution with shape1=4, shape2=7. What is
the p-value?
0.18573722 0.41073334 0.56355831 0.06673358 0.43762574
0.45158744 0.27369696
0.27787527 0.27522373 0.22834730 0.28829185 0.21342879
0.24438748 0.37434856
0.53836814 0.34561632 0.28320219 0.22540641 0.23575321
0.38607398 0.28625720
0.29384326 0.44312820 0.25625404 0.15563416 0.46424265
0.21000100 0.36114007
0.22198265 0.56719777

Use KS test to determine if the following two samples come from
the same distribution. What is the p-value?
> x1
1.4745039 0.6887191 0.7039077 0.6874590 0.3869872 0.6676840
2.1579876 1.2077449
0.6374479 0.8155020 0.6048739 0.7791121 1.1239440 0.2822348
1.1090178 0.4214001
1.1184735 1.1494251 1.2954266 1.2083231
> x2
0.5328365 0.1981889 0.7243260 1.1050412 0.6593431 0.7068702
0.9887464 0.4788393
0.7510702 0.5284408 0.7018747 0.6859908 0.2629962 0.7042702
0.7036941 0.9767885
1.1382272 2.6636804 1.4457343 0.2567961

3. What is the distribution of, in t-test?
4. What is the distribution of, in F-test?

You are given a transition matrix P. Find the
steady-state distribution vector. HINT [See Example 4.]
A) P =
5/6
1/6
7/9
2/9
B) P =
1/5
4/5
0
5/8
3/8
0
4/7
0
3/7

Use the t-distribution and the sample results to
complete the test of the hypotheses. Use a 5% significance level.
Assume the results come from a random sample, and if the sample
size is small, assume the underlying distribution is relatively
normal.
Test Ho : μ=120 vs Ha : μ<120 using the sample results x¯=112.3,
s=18.4, with n=100.
a) Give the test statistic and the p-value
Test statistic = _____
P-value = _____

(1) Consider a Chi-square distribution with degrees of freedom,
df =7 I What is the mean?; II. the standard deviation, for this
distribution?
(2) Consider a Chi-square distribution for a categorical
variable with 4 levels. I. What is the degrees of freedom for this
distribution? II. The chi-square test statistic was calculated to
be 8.012. What is the p-value for this distribution?

Group1:[100,250,50,80,150,150]
Group2:[112,240,58,82,165,180]
(a) Use signed rank test to see if there is a difference between
the two groups, state hypothesis, calculate test statistic and find
the p value by normal approximation

Use the normal distribution and the given sample results to
complete the test of the given hypotheses. Assume the results come
from a random sample and use a 5% significance level. Test H0 :
p=0.5 vs Ha : p>0.5 using the sample results p^=0.56 with n=50
Round your answer for the test statistic to two decimal places, and
your answer for the p-value to three decimal places.
Test statistic:
p-value:

Use the normal distribution and the given sample results to
complete the test of the given hypotheses. Assume the results come
from a random sample and use a 5% significance level.
Test H0 : p=0.25 vs Ha : p<0.25 using the sample results
p^=0.17 with n=100
Round your answer for the test statistic to two decimal places,
and your answer for the p-value to three decimal places.
test statistic=
p value=

Use the normal distribution and the given sample results to
complete the test of the given hypotheses. Assume the results come
from a random sample and use a 5% significance level.
Test H0 : p = 0.25 vs Ha : p < 0.25 using the sample results p^
= 0.16 with n = 100
Round your answer for the test statistic to two decimal places, and
your answer for the p-value to three decimal places.
test statistic=________________________
p-value=______________________

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