Question
In: Math
1. For a data set with 3 variables and 3 observations, suppose Xbar, the sample mean...
1. For a data set with 3 variables and 3 observations, suppose Xbar, the sample mean vector is [5, 3, 4]’. Let b’ = (1 1 1) and c’ = (1 2 -3).
The sample covariance matrix is given as, S = ( 13 −3.5 1.5; −3.5 1 −1.5 ; 1.5 −1.5 3 )
(a) Find the sample mean and variance for b’X and c’X.
(b) Find the sample mean and variance for c’X.
(c) Find the covariance between b’X and c’X.
Solutions
milcah answered 1 year agoRelated Solutions
Suppose you have a sample of 36 observations with the sample mean = 2 and the...
Suppose you have a sample of 36 observations with the sample
mean = 2 and the sample standard deviation = 7. Compute the
t-statistic corresponding to these values for the null hypothesis
that mean = 0. Test two-sided alternative hypothesis that mean 6=
0. Do you reject the null hypothesis at p = 0:05? At p = 0:01? If
the sample size is reduced to 25, do you get the same
conclusions?
These data are observations collected using a completely randomized design. Sample 1 Sample 2 Sample 3...
These data are observations collected using a completely
randomized design.
Sample 1
Sample 2
Sample 3
4
4
2
2
3
0
4
5
2
3
2
1
2
6
(a) Calculate CM and Total SS. (Round your answer for CM to six
decimal places and your Total SS to four decimal places.
(b) Calculate SST and MST. (Round your answers to four decimal
places.)
(c) Calculate SSE and MSE. (Round your answers to four decimal
places.)
(d) Construct an...
Suppose you calculated the mean, median, mode, and sample standard deviation of a data set. The...
Suppose you calculated the mean, median, mode, and sample
standard deviation of a data set. The results are shown below.
Mean: 44
Median: 31
Mode: 46
Sample Standard Deviation: 2
If each number in the data set was decreased by 4 units, what would
be the new values of these statistics?
Fill in your results below.
New Mean:
New Median:
New Mode:
New Sample Standard Deviation:
Sample Mean Suppose that ?1 ......?n are random variables, each distributed N(5,9) The sample size is...
Sample Mean Suppose that ?1 ......?n are random variables, each
distributed N(5,9) The sample size is 100.
(a)Calculate the mean and standard deviation of sample mean
?̅.
(b)Show Prob(4.7<?̅<5.3).
SHOW ALL WORK please
1) Suppose a normally distributed set of data has a mean of 179 and a standard...
1) Suppose a normally distributed set of data has a mean of 179
and a standard deviation of 17. Use the 68-95-99.7 Rule to
determine the percent of scores in the data set expected to be
below a score of 213. Give your answer as a percent and includeas
many decimal places as the 68-95-99.7 rule dictates. (For example,
enter 99.7 instead of 0.997.)
2) Suppose a normally distributed set of data with 2800
observations has a mean of 100...
Exercise 10-3 A sample of 35 observations is selected from a normal population. The sample mean...
Exercise 10-3
A sample of 35 observations is selected from a normal
population. The sample mean is 26, and the population standard
deviation is 4. Conduct the following test of hypothesis using the
.05 significance level.
H0 : μ ≤ 25
H1 : μ > 25
(a)
Is this a one- or two-tailed test?
"Two-tailed"-the alternate hypothesis is different from
direction.
"One-tailed"-the alternate hypothesis is greater than
direction.
(b)
What is the decision rule? (Round your answer to 2...
Consider the following sample of four observations of variables Y and Z Y 3 6 5...
Consider the following
sample of four observations of variables Y and Z
Y
3
6
5
9
Z
9
12
13
16
The sample covariance
of Y and Z is: (round to two decimal places)
a.
6.25
b.
7.55
c.
5.13
d.
6.83
e.
4.55
3. Take the mean and standard deviation of data set A calculated in problem 1 and...
3. Take the mean and standard deviation of data set A
calculated in problem 1 and assume that they are population
parameters (μ and σ) known for the variable fish length in a
population of rainbow trouts in the Coldwater River. Imagine that
data set B is a sample obtained from a different population in Red
River (Chapter 6 problem!).
a) Conduct a hypothesis test to see if the mean fish length in the
Red River population is different from...
3. Take the mean and standard deviation of data set A calculated in problem 1 and...
3. Take the mean and standard deviation of data
set A calculated in problem 1 and assume that they are population
parameters (μ and σ) known for the variable fish length in a
population of rainbow trouts in the Coldwater River. Imagine that
data set B is a sample obtained from a different
population in Red River (Chapter 6 problem!).
Conduct a hypothesis test to see if the mean fish length in the
Red River population is different from the...
3. Take the mean and standard deviation of data set A calculated in problem 1 and...
3. Take the mean and standard deviation of data set A calculated
in problem 1 and assume that they are population parameters (μ and
σ) known for the variable fish length in a population of rainbow
trouts in the Coldwater River. Imagine that data set B is a sample
obtained from a different population in Red River (Chapter 6
problem!). a) Conduct a hypothesis test to see if the mean fish
length in the Red River population is different from...
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