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Assigment questions have been linked in the pdf, for the datasheet my student number is B XXXXXXXXXXyou can enter it in the green column

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Statistics and Probability
Assignment on Hypothesis Testing
January 30, 2023
Instructions
This document contains the questions for your assignment project
on Statistical Testing. The questions refer to the data given in the
individual worksheets in Excel document ‘Assignment Datasets.xlsx’.
Please read the following points.
1. All submissions must be in the form of PDF documents. Spread-
sheets exported to PDF will be accepted, but calculations must
e annotated or explained.
2. It is up to you how you do the calculations in each question, but
you must explain how you a
ived at your answer for any given
calculation. This can be done with a written explanation and
y using the relevant equations, along with showing the results
of intermediate stages of the calculations. In other words, you
need to show that you know how to do a calculation for a statistic
other than using spreadsheet functions.
3. Each one of the questions involves a statistical test. Marks within
each question will generally be awarded for:
1
• Deciding which statistical test to use,
• Framing your Hypotheses and proper conclusions,
• Identifying the parameters for the test and
• Showing a reasonable level of clarity, detail and explanation
in the calculations needed to ca
y out the test.
4. The data you have been given is in the worksheets of an Excel
spreadsheet. This spreadsheet is locked against editing. Please
to not try to circumvent this; if you wish to use a spreadsheet to
do your calculations, you should copy and paste your data into
your own spreadsheet and work with that.
Question 1
The lifetimes (in units of 106 seconds) of certain satellite components
are shown in the frequency distribution given in ‘Dataset1’.
1. Draw a frequency polygon, histogram and cumulative frequency
polygon for the data.
2. Calculate the frequency mean, the frequency standard deviation,
the median and the first and third quartiles for this grouped data.
3. Compare the median and the mean and state what this indicates
about the distribution. Comment on how the answer to this ques-
tion relates to your frequency polygon and histogram.
4. Explain the logic behind the equations for the mean and standard
deviation for grouped data, starting from the original equations
for a simple list of data values. (This does not just mean ’explain
how the equations are used’.)
Page 2
5. Ca
y out an appropriate statistical test to determine whether the
data is normally distributed.
Question 2
A manufacturer of metal plates makes two claims concerning the
thickness of the plates they produce. They are stated here:
• Statement A: The mean is 200mm
• Statement B: The variance is 1.5mm2.
To investigate Statement A, the thickness of a sample of metal plates
produced in a given shift was measured. The values found are listed
in Part (a) of worksheet ‘Dataset2’, with millimetres (mm) as unit.
1. Calculate the sample mean and sample standard deviation for the
data in Part (a) of ’Dataset2’. Explain why we are using the phrase
’sample’ mean or sample’ standard deviation.
2. Set up the framework of an appropriate statistical test on State-
ment A. Explain how knowing the sample mean before ca
ying
out the test will influence the structure of your test.
3. Ca
y out the statistical test and state your conclusions.
To investigate the second claim, the thickness of a second sample of
metal sheets was measured. The values found are listed in Part (b) of
worksheet ‘Dataset2’, with millimetres (mm) as unit.
1. Calculate the sample mean and then the sample variance and
standard deviation for the data in Part (b).
Page 3
2. Set up the framework of an appropriate statistical test on State-
ment B. Explain how knowing the sample variance before ca
y-
ing out the test would influence the structure of your test.
3. Ca
y out the statistical test and state your conclusions.
Question 3
A manager of an inter-county hurling team is concerned that his team
lose matches because they ‘fade away’ in the last ten minutes. He
has measured GPS data showing how much ground particular players
cover within a given time period; this is the data in list (a) in worksheet
‘Dataset3’. He has acquired the co
esponding data from an opposing,
more successful team, which is given in list (b).
1. Calculate the sample mean and sample standard deviation for the
two sets of data.
2. Set up the frame work of an appropriate statistical test to deter-
mine whether there is a difference in the distances covered by the
two groups of players.
3. Explain how having the results of the calculations above in ad-
vance of doing your statistical test will influence the structure of
that test.
4. Ca
y out the statistical test and state your conclusions.
Question 4
A study was ca
ied out to determine whether the resistance of the
control circuits in a machine are lower when the machine motor is
Page 4
unning. To investigate this question, a set of the control circuits was
tested as follows. Their resistance was measured while the machine
motor was not running for a certain period of time and then again
while the motor was running. The values found are listed in worksheet
‘Dataset4’, with kilo-Ohms as the unit of measurement.
1. Set up the structure of an appropriate statistical test to determine
whether the resistance of the control circuit in a machine are
lower when the machine motor is running.
2. Explain how the order of subtraction chosen to calculate the dif-
ferences will influence the structure of the test.
3. Give a reason why the data is measured with the engine not run-
ning first and then with the engine running.
4. Explain how knowing the mean of the differences in advance will
influence the structure of your statistical test.
5. Ca
y out the statistical test and state your conclusions.
Question 5
A study was ca
ied out to determine the influence of a trace element
found in soil on the yield of potato plants grown in that soil, defined as
the weight of potatoes produced at the end of the season. A large field
was divided up into 14 smaller sections for this experiment. For each
section, the experimenter recorded the amount of the trace element
found (in milligrams per metre squared) and the co
esponding weight
of the potatoes produced (in kilograms). This information is presented
in the worksheet ‘Dataset5’ in the Excel document. Define X as the
trace element amount and Y as the yield.
Page 5
1. Draw a scatterplot of your data set.
2. Calculate the coefficients of a linear equation to predict the yield
Y as a function of X.
3. Calculate the co
elation coefficient for the paired data values.
4. Set up the framework for an appropriate statistical test to estab-
lish if there is a co
elation between the amount of the trace ele-
ment and the yield. Explain how having the scatterplot refe
ed
to above and having the value of r in advance will influence the
structure of your statistical test.
5. Ca
y out and state the conclusion of your test on the co
elation.
6. Comment on how well the regression equation will perform based
on the results above.
Question 6
A multinational corporation is conducting a study to see how its em-
ployees in five different countries respond to three gifts in an incentive
scheme. The numbers of employees who choose each of the three gifts
(G1 to G3) in each of the five countries (A to E) are given in the table
in ‘Dataset6’ in the Excel document.
1. Set up the structure of an appropriate statistical test to deter-
mine whether the data supports a link between choice of gift and
country, including the statistic to be used.
2. Ca
y out this test, showing clearly in your work how the expected
values are calculated for your test statistic.
Page 6

Dataset 1
        Assignment : Hypothesis Testing
        Type the last three digits of your student number in the green cell:
                                678
         XXXXXXXXXX
         XXXXXXXXXX        328
        Dataset 1
            7
    20        Groups            Frequencies
    0.1        300    to    307    12     XXXXXXXXXX
    0.8        307    to    314    18     XXXXXXXXXX
    62    0.67    314    to    321    44     XXXXXXXXXX
    0.8    0.76    321    to    328    88     XXXXXXXXXX
        1    328    to    335    86     XXXXXXXXXX
        0.73    335    to    342    41     XXXXXXXXXX
     XXXXXXXXXX    0.45    342    to    349    15     XXXXXXXXXX
     XXXXXXXXXX    0.42    349    to    356    9     XXXXXXXXXX
     XXXXXXXXXX    0.14
     XXXXXXXXXX    0
     XXXXXXXXXX
     XXXXXXXXXX
     XXXXXXXXXX
     XXXXXXXXXX
&"Helvetica Neue,Regular"&12&K000000&P    
Dataset 2
     XXXXXXXXXX    Assignment : Hypothesis Testing
     XXXXXXXXXX
     XXXXXXXXXX    Dataset 2
    20
    0.1    Part (a)
        207.20    202.13    196.93    198.16    197.74    198.15
    0.8    207.65    203.68    197.13    197.06    196.60    197.55
        208.93    202.22    198.63    197.09    197.40    198.36
        207.51    201.32    197.97    198.31    198.04    198.78
        206.02    200.07    196.67    199.85    199.05    200.31
        205.84    199.09    197.67    198.40    200.32    199.29
        204.36    198.89    196.90    197.34    199.11    200.46
        Part (b)
        203.64    197.56    198.07    198.70    198.13    202.00
        203.23    198.43    199.61    197.65    198.25    200.55
        198.56    199.07    199.70    199.13    203.00    204.23
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
&"Helvetica Neue,Regular"&12&K000000&P    
Dataset 3
     XXXXXXXXXX    Assignment : Hypothesis Testing
     XXXXXXXXXX
     XXXXXXXXXX    Dataset 3
    20
    0.1    12
    1500    List (a)
    10    1571.96    1521.34    1469.33    1481.63    1477.40    1481.47    1500.52
    0.8    1576.48    1536.76    1471.25    1470.57    1465.99    1475.55    1470.84
        1589.26    1522.16    1486.27    1470.91    1473.99    1483.60    1504.37
        1575.09    1513.18    1479.72    1483.13    1480.39    1487.82
        List (b)
        1548.18    1488.69    1454.72    1486.54    1478.50    1491.10    1477.71
        1546.39    1478.92    1464.75    1472.01    1491.17    1480.93    1489.03
        1531.61    1476.90    1457.05    1461.36    1479.14    1492.60    1472.54
        1524.35    1463.57    1468.71    1474.99    1469.29    1508.04    1484.82
        1520.35    1472.29    1484.15    1464.52    1470.48    1493.46
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
&"Helvetica Neue,Regular"&12&K000000&P    
Dataset 4
     XXXXXXXXXX
     XXXXXXXXXX    Assignment : Hypothesis Testing
    20    Dataset 4
    0.1
    0.8        Resistance:
    14
    0.8        Motor running    Motor not running
        0.86    15.72    15.12     XXXXXXXXXX    0.2
        0.9    15.80    15.18     XXXXXXXXXX    0.18
     XXXXXXXXXX    1    16.00    15.27     XXXXXXXXXX    0.07
     XXXXXXXXXX    0.88    15.76    15.10     XXXXXXXXXX    0.14
     XXXXXXXXXX    0.76    15.52    14.74     XXXXXXXXXX    0.02
     XXXXXXXXXX    0.75    15.50    14.74     XXXXXXXXXX    0.04
     XXXXXXXXXX    0.63    15.26    14.62     XXXXXXXXXX    0.16
     XXXXXXXXXX    0.57    15.14    14.45     XXXXXXXXXX    0.11
     XXXXXXXXXX    0.54    15.08    14.28     XXXXXXXXXX    0
     XXXXXXXXXX    0.45    14.90    14.18     XXXXXXXXXX    0.08
     XXXXXXXXXX    0.57    15.14    14.36     XXXXXXXXXX    0.02
     XXXXXXXXXX    0.45    14.90    14.21     XXXXXXXXXX    0.11
     XXXXXXXXXX    0.38    14.76    14.20     XXXXXXXXXX    0.24
     XXXXXXXXXX    0.28    14.56    13.88     XXXXXXXXXX    0.12
     XXXXXXXXXX    0.2    14.40    13.63     XXXXXXXXXX    0.03
     XXXXXXXXXX    0.18    14.36    13.59     XXXXXXXXXX    0.03
     XXXXXXXXXX    0.07    14.14    13.47     XXXXXXXXXX    0.13
     XXXXXXXXXX    0.14    14.28    13.74     XXXXXXXXXX    0.26
     XXXXXXXXXX    0.72    15.44    14.78     XXXXXXXXXX    0.14
     XXXXXXXXXX    0.72    15.44    14.69     XXXXXXXXXX    0.05
&"Helvetica Neue,Regular"&12&K000000&P    
Dataset 5
     XXXXXXXXXX
     XXXXXXXXXX    Assignment : Hypothesis Testing
    0.8
    28    Dataset 5        132
    0.2            0.15
                4.8
    62        Additive    Yield
     XXXXXXXXXX    1    77    119.68     XXXXXXXXXX    0.48
    0.2     XXXXXXXXXX    74.37    119.26     XXXXXXXXXX    0.31
    62.2     XXXXXXXXXX    75.1    119.78     XXXXXXXXXX    0.44
     XXXXXXXXXX     XXXXXXXXXX    76.07    119.29     XXXXXXXXXX    0.37
     XXXXXXXXXX     XXXXXXXXXX    73.74    118.88     XXXXXXXXXX    0.21
     XXXXXXXXXX     XXXXXXXXXX    72.83    119.49     XXXXXXXXXX    0.31
     XXXXXXXXXX     XXXXXXXXXX    71.81    118.92     XXXXXXXXXX    0.16
     XXXXXXXXXX     XXXXXXXXXX    70.94    118.72     XXXXXXXXXX    0.09
     XXXXXXXXXX     XXXXXXXXXX    68.53    119.08     XXXXXXXXXX    0.09
     XXXXXXXXXX     XXXXXXXXXX    65.94    119.04     XXXXXXXXXX    0
     XXXXXXXXXX     XXXXXXXXXX    68.11    119.29     XXXXXXXXXX    0.12
     XXXXXXXXXX     XXXXXXXXXX    70.43    119.85     XXXXXXXXXX    0.31
     XXXXXXXXXX     XXXXXXXXXX    70.61    120.5     XXXXXXXXXX    0.45
     XXXXXXXXXX     XXXXXXXXXX    69.07    120.06     XXXXXXXXXX    0.31
     XXXXXXXXXX
     XXXXXXXXXX
     XXXXXXXXXX
&"Helvetica Neue,Regular"&12&K000000&P    
Dataset 6
        Assignment : Hypothesis Testing
    15    Dataset 6
    0.12
            G1    G2    G3
        A    10    13    14
        B    18    11    6
    School    C    16    20    17
        D    12    25    13
        E    5    22    14
         XXXXXXXXXX
         XXXXXXXXXX    0.8     XXXXXXXXXX     XXXXXXXXXX
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
             XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
             XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
             XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
                 XXXXXXXXXX
             XXXXXXXXXX
             XXXXXXXXXX
&"Helvetica Neue,Regular"&12&K000000&P    
Reference
            3
            678
        Student numbers    Last3        Seed value
        B XXXXXXXXXX    204    1    0.8
        B XXXXXXXXXX    224    1
        B XXXXXXXXXX    476    1
        B XXXXXXXXXX    935    0
        B XXXXXXXXXX    479    1
        B XXXXXXXXXX    662    1
        B XXXXXXXXXX    463    1
        B XXXXXXXXXX    837    0
        B XXXXXXXXXX    309    1
        B XXXXXXXXXX    219    1
        B XXXXXXXXXX    85    1
        B XXXXXXXXXX    353    1
        B XXXXXXXXXX    414    1
        B XXXXXXXXXX    800    0
        B XXXXXXXXXX    347    1
        B XXXXXXXXXX    307    1
        B XXXXXXXXXX    44    1
        B XXXXXXXXXX    110    1
        B XXXXXXXXXX    967    0
        B XXXXXXXXXX    464    1
        B XXXXXXXXXX    570    1
        B XXXXXXXXXX    650    1
        B XXXXXXXXXX    882    0
        B XXXXXXXXXX    304    1
        B XXXXXXXXXX    276    1
        B XXXXXXXXXX    488    1
        B XXXXXXXXXX    585    1
        B XXXXXXXXXX    295    1
        B XXXXXXXXXX    300    1
        B XXXXXXXXXX    346    1
        B XXXXXXXXXX    534    1
        B XXXXXXXXXX    448    1
        B XXXXXXXXXX    233    1
        B XXXXXXXXXX    32    1
        B XXXXXXXXXX    458    1
        B XXXXXXXXXX    56    1
        B XXXXXXXXXX    582    1
        B XXXXXXXXXX    439    1
        B XXXXXXXXXX    196    1
        B XXXXXXXXXX    627    1
        B XXXXXXXXXX    455    1
        B XXXXXXXXXX    814    0
        B XXXXXXXXXX    322    1
        B XXXXXXXXXX    901    0
        B XXXXXXXXXX    724    0
        B XXXXXXXXXX    328    1
        B XXXXXXXXXX    853    0
        B XXXXXXXXXX    7    1
        B XXXXXXXXXX    463    1
        B XXXXXXXXXX    522    1
        B XXXXXXXXXX    878    0
        B XXXXXXXXXX    983    0
        B XXXXXXXXXX    503    1
        B XXXXXXXXXX    367    1
        B XXXXXXXXXX    975    0
        B XXXXXXXXXX    51    1
        B XXXXXXXXXX    146    1
        B XXXXXXXXXX    765    0
        B XXXXXXXXXX    210    1
        B XXXXXXXXXX    959    0
        B XXXXXXXXXX    834    0
        B XXXXXXXXXX    572    1
        B XXXXXXXXXX    67    1
        B XXXXXXXXXX    640    1
        B XXXXXXXXXX    863    0
        B XXXXXXXXXX    876    0
        B XXXXXXXXXX    39    1
        B XXXXXXXXXX    956    0
        B XXXXXXXXXX    73    1
        B XXXXXXXXXX    969    0
        B XXXXXXXXXX    10    1
        B XXXXXXXXXX    688    0
        B XXXXXXXXXX    187    1
        B XXXXXXXXXX    882    0
        B XXXXXXXXXX    112    1
        B XXXXXXXXXX    282    1
        B XXXXXXXXXX    654    1
        B XXXXXXXXXX    373    1
        B XXXXXXXXXX    176    1
        B XXXXXXXXXX    24    1
        B XXXXXXXXXX    972    0
        B XXXXXXXXXX    339    1
        B XXXXXXXXXX    312    1
        B XXXXXXXXXX    10    1
        B XXXXXXXXXX    95    1
        B XXXXXXXXXX    610    1
        B XXXXXXXXXX    198    1
        B XXXXXXXXXX    430    1
        B XXXXXXXXXX    754    0
        B XXXXXXXXXX    841    0
        B XXXXXXXXXX    311    1
        B XXXXXXXXXX    946    0
        B XXXXXXXXXX    852    0
        B XXXXXXXXXX    676    1
        B XXXXXXXXXX    770    0
        B XXXXXXXXXX    18    1
        B XXXXXXXXXX    255    1
        B XXXXXXXXXX    502    1
        B XXXXXXXXXX    838    0
        B XXXXXXXXXX    111    1
        B XXXXXXXXXX    30    1
&"Helvetica Neue,Regular"&12&K000000&P
Answered 1 days After May 15, 2023

Solution

Monica answered on May 17 2023
28 Votes
Sheet1
                G1    G2    G3
            A    10    13    14
            B    18    11    6
            C    16    20    17
            D    12    25    13
            E    5    22    14
                G1    G2    G3    Total
            A    10    13    14    37
            B    18    11    6    35
            C    16    20    17    53
            D    12    25    13    50
            E    5    22    14    41
            Total    61    91    64    216
        E        10.4490740741    15.587962963    10.962962963
                9.8842592593    14.7453703704    10.3703703704
                14.9675925926    22.3287037037    15.70370...
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