Let X 1 , X 2 , ... , X n be independent random variables having an unknown continuous distribution function F. and let Y 1 , Y 2 , ... , Y m be independent random variables having an unknown continuous distribution function G. Now order those n + m variables, and let I i = { 1 if the i th smallest of the n + m variables is from the X sample 0 otherwise The random variable R = ∑ i = 1 n + m i I i is the sum of the ranks of the X sample and is the basis of a standard statistical procedure (called theWilcoxon sum-of-ranks test) for testing whether F and G are identical distributions. This test accepts the hypothesis that F = G when R is neither too large nor too small. Assuming that the hypothesis of equality is in fact correct, compute the mean and variance of R. Hint: Use the results of Example 3e.
Let X 1 , X 2 , ... , X n be independent random variables having an unknown continuous distribution function F. and let Y 1 , Y 2 , ... , Y m be independent random variables having an unknown continuous distribution function G. Now order those n + m variables, and let I i = { 1 if the i th smallest of the n + m variables is from the X sample 0 otherwise The random variable R = ∑ i = 1 n + m i I i is the sum of the ranks of the X sample and is the basis of a standard statistical procedure (called theWilcoxon sum-of-ranks test) for testing whether F and G are identical distributions. This test accepts the hypothesis that F = G when R is neither too large nor too small. Assuming that the hypothesis of equality is in fact correct, compute the mean and variance of R. Hint: Use the results of Example 3e.
Let
X
1
,
X
2
,
...
,
X
n
be independent random variables having an unknown continuous distribution function F. and let
Y
1
,
Y
2
,
...
,
Y
m
be independent random variables having an unknown continuous distribution function G. Now order those
n
+
m
variables, and let
I
i
=
{
1
if the
i
th smallest of the
n
+
m
variables is from the
X
sample
0
otherwise
The random variable
R
=
∑
i
=
1
n
+
m
i
I
i
is the sum of the ranks of the X sample and is the basis of a standard statistical procedure (called theWilcoxon sum-of-ranks test) for testing whether F and G are identical distributions. This test accepts the hypothesis that
F
=
G
when R is neither too large nor too small. Assuming that the hypothesis of equality is in fact correct, compute the mean and variance of R.
Hint: Use the results of Example 3e.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
3. A different 7-Eleven has a bank of slurpee fountain heads. Their available flavors are as follows: Mountain
Dew, Mountain Dew Code Red, Grape, Pepsi and Mountain Dew Livewire. You fill five different cups full
with each type of flavor. How many different ways can you arrange the cups in a line if exactly two Mountain
Dew flavors are next to each other?
3.2.1
Answer questions 8.3.3 and 8.3.4 respectively
8.3.4 .WP An article in Medicine and Science in Sports and
Exercise [“Electrostimulation Training Effects on the Physical Performance of Ice Hockey Players” (2005, Vol. 37, pp.
455–460)] considered the use of electromyostimulation (EMS) as
a method to train healthy skeletal muscle. EMS sessions consisted of 30 contractions (4-second duration, 85 Hz) and were carried
out three times per week for 3 weeks on 17 ice hockey players.
The 10-meter skating performance test showed a standard deviation of 0.09 seconds. Construct a 95% confidence interval of the
standard deviation of the skating performance test.
8.6.7 Consider the tire-testing data in Exercise 8.2.3. Compute a 95% tolerance interval on the life of the tires that has confidence level 95%. Compare the length of the tolerance interval with the length of the 95% CI on the population mean. Which interval is shorter? Discuss the difference in interpretation of these two intervals.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.