Question

Data

For Tasks 1-8, consider the following data:

7.2, 1.2, 1.8, 2.8, 18, -1.9, -0.1, -1.5, 13.0, 3.2, -1.1,
7.0, 0.5, 3.9, 2.1, 4.1, 6.5

In Tasks 1-8 you are asked to conduct some computations
regarding this data. The computation should be carried out
manually. All the steps that go into the computation should be
presented and explained. (You may use R in order to verify your
computation, but not as a substitute for conducting the manual
computations.)

A Random Variable

In Tasks 9-18 you are asked to conduct some computations
regarding a random variable. Use the (incomplete) table below as
the definition of this random variable (after you fill in the
blank). The sample space of a random variable is comprised of the
integers 0, 1, 2, 3, 4, 5, and 6. The probabilities of each value
are shown in the table below (with one missing value).

Value

0

1

2

3

4

5

6

Probability

.10

.15

.25

.10

.10

.15

A Population

For Tasks 19-21, use the file called "pop3.csv" found here.
That file contains information about time to failure of an entire
production of some computer parts. The file contains two variables,
"type" and "time", each measured over the 100,000 members of the
population. The variable "type" is a factor, with three levels,
"a", "b" and "c", and the variable "time" is numeric. If the value
of time is 4, that means that the part lasted 4 units of time
(years?) before a failure occurred. You should treat the content of
this file as the information from an entire population.

Save the file on your computer and read the data stored in the
file into R. If you have trouble loading the data into R, email
your instructor immediately—don't worry if you think you will find
the answer 1 minute after sending the email—just send the email.
Tasks 19-21 refer to the information in the file.

Submitting the Assignment

For the assignment you should complete the following tasks.
Tasks 1-8 refer to the sequence of 17 data values presented above,
Tasks 9-18 refer to the random variable and Tasks 19-XXX21 refer to
the information of a population of computer parts that is stored in
the file "pop3.csv". Your answers should be short and clear.

We recommend that you copy and paste the tasks below into the
assignment submission area. You can then write your answers to the
tasks in the designated positions that are marked in the
text:

Tasks

Data:

1. Using the list of 17 numbers at the top of the page, the
median of this data, rounded to two decimal places, is:_____.

2. If you find the median using the original method (paper and
pencil), you have to arrange the values into numeric order
(True/False).______________________

3. The interquartile range for this data is (round each value
to 3 decimal places):_______.

4. The formula for calculating the interquartile range
is_____________ (show the formula and a citation to the source that
you used).

5. Using techniques that we have studied in this course, the
upper and lower cutoff points (rounded to three decimal places) for
identifying outliers (in the given data sample) are: ________ and
________ (this is not a request to show any outliers--just the
cutoff points that would determine what constitutes an outlier).
You may round to three decimal places.

6. The summary() command shows a list of outliers, if there
are any (True/False):______________________

7. The list of outlier values is:_____________ (if there are
none, write "NA").

8. The standard deviation of the list of 17 numbers is (round
to 3 decimal places): ______________

A Random Variable:

9. The missing probability value (under the number 4) in the
random variable table above is:_______

10. The sum of the probabilites in the second row of any
random variable table like the one above should equal (round to 3
decimal places):
_______________________________________________.

11. Read section 4.4.1 in the book (Yakir, 2011). Do the
numbers in the table above (for the random variable) represent a
data sample (Yes/No)?____

12. In the random variable table shown above, the value in the
second row represents the cumulative probability of the
corresponding values in the first row (True/False) _________

13. The probability that a randomly selected value from this
random value will be less than or equal to 3 is :_____.

14. What is the probability that a randomly selected value
from the random variable would be exactly 1.5? ___________ .

15. Review section 4.4 in the book (Yakir, 2011), especially
pages 57—58. The expectation of the random variable
is:______.

16. To find the expectation of a random variable by using a
relative frequency table, you can add the values in the first row
of the table and divide by the number of columns in the table
(True/False)_________.

17. Study Yakir (2011) pp. 57-59 and solved problems
4.1.6-4.1.8. The (population) standard deviation of the random
variable above is (round to 3 decimal places):_______ (hint, you
can not put values from the table into the sd() function because
the sd() function does not adjust for the probabilities).

18. If you have already calculated the standard deviation of a
data sample, what is the next thing to do to find the variance:
______________________________.

A Population:

19. Determine how many observations in the pop3.csv file are
of type a: _______.

20. Using the appropriate R function with the defaul options,
what is the median of the time column of pop3 (round to 3 decimal
places): ______________________________.

21. What is the variance of the time column of pop3 (rounded
to three decimal places)? _______

Answer #1

Data is :

7.2, 1.2, 1.8, 2.8, 18, -1.9, -0.1, -1.5, 13.0, 3.2, -1.1, 7.0, 0.5, 3.9, 2.1, 4.1, 6.5

The data arranged inascending order is

-1.9,-1.5,-1.1,-0.1,0.5,1.2,1.8,2.1,**2.8**,3.2,3.9,4.1,6.5,7.0,7.2,13.0,18

Answers :

1. Using the list of 17 numbers at the top of the page, the
median of this data, rounded to two decimal places, is:
**2.8**

Solution : Md = (n+1)/2 = 9th observation of the arranged data

Median = 2.8

2. If you find the median using the original method (paper and
pencil), you have to arrange the values into numeric order :
**True**

**3)** The interquartile range for this data is
(round each value to 3 decimal places) : **6.550**

First Quartile = (n+1)/4 = 4.5th observation

Q1 =-0.1 +0.5(0.5-(-0.1) = 0.2

Thrid Quartile = 3(n+1)/4 = 13.5 th observation

Q3 = 6.5+0.5(7-6.5) = 6.75

Inter Quartile Range = Q3-Q1 = 6.75- 0.2 = 6.550

Q4 ) The formula for calculating the interquartile range is IQR = Q3-Q1

Q5) Upper Cut Off = Q3+1.5 IQR =6.75+1.5*6.55 = 16.575

Lower Cut Off = Q1- 1.5IQR = 0.2-1.5*6.55 =-9.625

6) True

7) The outlier is 18 since it is greater than Upper Cut off 16.575

8) The Standard deviation of the list of numbers is

Consider the following competing hypotheses and accompanying
sample data drawn independently from normally distributed
populations. (You may find it useful to reference the
appropriate table: z table or t
table)
H0: μ1 −
μ2 ≥ 0
HA: μ1 −
μ2 < 0
x−1x−1 = 246
x−2x−2 = 250
s1 = 26
s2 = 22
n1 = 8
n2 = 8
a-1. Calculate the value of the test statistic
under the assumption that the population variances are equal.
(Negative values should...

Consider the following competing hypotheses and accompanying
sample data drawn independently from normally distributed
populations. (You may find it useful to reference the
appropriate table: z table or t
table)
H0: μ1 −
μ2 ≥ 0
HA: μ1 −
μ2 < 0
x−1x−1 = 232
x−2x−2 = 259
s1 = 30
s2 = 20
n1 = 6
n2 = 6
a-1. Calculate the value of the test statistic
under the assumption that the population variances are equal.
(Negative values should...

Consider the following time series data.
Week 1 2 3 4 5 6
Value 18 13 15 13 15 15
(b)
Develop a three-week moving average for this time series.
Compute MSE and a forecast for week 7.
If required, round your answers to two decimal places.
(c) Use α = 0.2 to compute the
exponential smoothing values for the time series. Compute MSE and a
forecast for week 7.
If required, round your answers to two decimal places.
(d)...

Consider the following data drawn independently from normally
distributed populations: (You may find it useful to
reference the appropriate table: z table
or t table)
x 1= 27.1
x2 = 30.3
σ12 = 89.5
σ22 = 92.3
n1 = 25
n2 = 31
a. Construct the 90% confidence interval for the difference
between the population means. (Negative values should be indicated
by a minus sign. Round all intermediate calculations to at least 4
decimal places and final answers to 2...

Consider the following sample data drawn independently from
normally distributed populations with unknown but equal population
variances. (You may find it useful to reference the
appropriate table: z table or t
table)
Sample 1
Sample 2
12.1
8.9
9.5
10.9
7.3
11.2
10.2
10.6
8.9
9.8
9.8
9.8
7.2
11.2
10.2
12.1
Click here for the Excel Data File
a. Construct the relevant hypotheses to test if
the mean of the second population is greater than the mean of the...

Data sets for the question below
Data Set G: Assume the population values are normally
distributed.
Random variable: x = weight of border collie in pounds
sample size = 25
34.1
40.8
36.0
34.9
35.6
43.4
35.4
29.3
33.3
37.8
35.8
37.4
39.0
38.6
33.9
36.5
37.2
37.6
37.3
37.7
34.9
33.2
36.2
33.5
36.9
Use Excel (or similar software) to create the tables. Then copy
the items and paste them into a Word document. The tables should be
formatted...

Consider the following data drawn independently from normally
distributed populations: (You may find it useful to
reference the appropriate table: z table
or t table)
x−1x−1 =
25.7
x¯2x¯2 =
30.6
σ12 = 98.2
σ22 = 87.4
n1 = 20
n2 = 25
Construct the 95% confidence interval for the difference between
the population means. (Negative values should be indicated
by a minus sign. Round all intermediate calculations to at least 4
decimal places and final answers to 2 decimal...

Consider the following competing hypotheses and accompanying
sample data drawn independently from normally distributed
populations. (You may find it useful to reference the
appropriate table: z table or t
table)
H0: μ1 −
μ2 = 0
HA: μ1 −
μ2 ≠ 0
x−1x−1 = 75
x−2x−2 = 79
σ1 = 11.10
σ2 = 1.67
n1 = 20
n2 = 20
a-1. Calculate the value of the test statistic.
(Negative values should be indicated by a minus sign. Round
all intermediate...

Consider the following competing hypotheses and accompanying
sample data drawn independently from normally distributed
populations. (You may find it useful to reference the
appropriate table: z table or t
table)
H0: μ1 −
μ2 = 0
HA: μ1 −
μ2 ≠ 0
x−1x−1 = 57
x−2x−2 = 63
σ1 = 11.5
σ2 = 15.2
n1 = 20
n2 = 20
a-1. Calculate the value of the test statistic.
(Negative values should be indicated by a minus sign. Round
all intermediate...

Consider the following competing hypotheses and accompanying
sample data drawn independently from normally distributed
populations. (You may find it useful to reference the
appropriate table: z table or t
table)
H0: μ1 −
μ2 = 0
HA: μ1 −
μ2 ≠ 0
x−1x−1 = 68
x−2x−2 = 80
σ1 = 12.30
σ2 = 1.68
n1 = 15
n2 = 15
a-1. Calculate the value of the test statistic.
(Negative values should be indicated by a minus sign. Round
all intermediate...

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