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You must enter the last three digits of your student number in the green cell of the first worksheet of your datasets spreadsheet document.

Be aware that the assignment excel document is locked against editing, to protect the mechanism by which I generate the numbers in your individual assignment. Do not attempt to get around this.

Please show a reasonable level of detail and explanation in your submission, so it is clear to anybody marking your work how you have arrived at your results. Remember, if your final answers to the questions are not correct, you will get more marks if your method is clear and it can be seen how much of your work was correct.

I am not accepting spreadsheet files in the online submission in order that they cannot be used to explain results; you should use a combination of the relevant equations and the English (or other human) language to explain how you arrived at your answer.

My student number is; B00102852.

Dataset 1 Assignment : Hypothesis Testing Type the last three digits of your student number in the green cell: 876 -1.0180741109 11.2000276957328 Dataset 1 7 20GroupsFrequencies 0.1300to307120.2768276259 0.9307to314194.4940491225 630.47314to3214228.5400756165 0.91321to3288571.6823966744 0.51328to3358571.6823966744 0335to3424228.5400756165 4.74195713520.07342to349194.4940491225 11.20002769570.57349to356110.2768276259 5.24507162110.84 -1.01807411090.33 -0.1966626297 5.9153709622 9.2432483616 2.9827781113 &"Helvetica Neue,Regular"&12&K000000&P Dataset 2 -50.1754024135Assignment : Hypothesis Testing -19.5384414639 17.6314507132Dataset 2 20 0.1Part (a) 204.27205.23200.62198.29199.44195.77 0.9205.40204.22200.75199.43198.39194.99 204.36203.86201.89198.36197.35195.07 203.26203.45200.84197.64196.53194.61 203.40203.00199.75197.39197.61195.63 204.48203.17199.65198.08198.35196.33 205.06203.12199.47198.29197.72196.89 Part (b) 203.96202.11199.03199.39197.67198.00 204.10201.72199.27199.31196.60197.46 203.11200.03200.39198.67199.00205.10 4.741957135210.1847418333-16.0165028249-29.2521165305-22.7033889221-43.6243826535 11.20002769574.4462433231-15.2575720788-22.7864817344-28.6985164327-48.0084692166 5.24507162112.4366288239-8.7985780979-28.8861625226-34.6345295835-47.5698604122 -1.01807411090.0682326145-14.7705257383-32.9612117723-39.2974204463-50.1754024135 -0.1966626297-2.4782295997-20.9838539374-34.3974272411-33.1117182115-44.3957891711 5.9153709622-1.5101266616-21.5285891938-30.4727064003-28.9010323745-40.4188922468 9.2432483616-1.8149198642-22.5660168753-29.2863057449-32.5095026793-37.2131984428 2.9827781113-7.5587995629-25.0316166939-22.985029217-32.7893840472-30.916436968 3.7703100996-9.7576414864-23.6752505192-23.4829778427-38.8616570183-34.0074895088 10.1847418333-16.0165028249-29.2521165305-22.7033889221-43.6243826535-33.6080197126 &"Helvetica Neue,Regular"&12&K000000&P Dataset 3 -50.1754024135Assignment : Hypothesis Testing -19.5384414639 17.6314507132Dataset 3 20 0.113.5 1500List (a) 101542.691552.261506.191482.921494.441457.651506.03 0.91554.051542.171507.531494.291483.891449.941483.91 1543.571538.641518.881483.561473.461450.711501.47 1532.561534.471508.381476.401465.261446.13 List (b) 1520.511516.501483.961460.371462.641442.801462.44 1531.251518.201483.001467.281470.041449.791486.59 1537.101517.661481.181469.361463.691455.421467.41 1526.101507.561476.841480.441463.201466.491486.77 1527.481503.701479.231479.561452.531461.06 4.741957135210.1847418333-16.0165028249-29.2521165305-22.7033889221-43.6243826535 11.20002769574.4462433231-15.2575720788-22.7864817344-28.6985164327-48.0084692166 5.24507162112.4366288239-8.7985780979-28.8861625226-34.6345295835-47.5698604122 -1.01807411090.0682326145-14.7705257383-32.9612117723-39.2974204463-50.1754024135 -0.1966626297-2.4782295997-20.9838539374-34.3974272411-33.1117182115-44.3957891711 5.9153709622-1.5101266616-21.5285891938-30.4727064003-28.9010323745-40.4188922468 9.2432483616-1.8149198642-22.5660168753-29.2863057449-32.5095026793-37.2131984428 2.9827781113-7.5587995629-25.0316166939-22.985029217-32.7893840472-30.916436968 3.7703100996-9.7576414864-23.6752505192-23.4829778427-38.8616570183-34.0074895088 &"Helvetica Neue,Regular"&12&K000000&P Dataset 4 -29.2521165305 11.2000276957Assignment : Hypothesis Testing 20Dataset 4 0.1 0.9Resistance: 14 0.9Motor runningMotor not running 0.8415.6815.47-1.51012666160.69 116.0015.78-1.81491986420.68 4.74195713520.8515.7015.34-7.55879956290.54 11.20002769570.715.4014.98-9.75764148640.48 5.24507162110.7215.4414.87-16.01650282490.33 -1.01807411090.8715.7415.19-15.25757207880.35 -0.19666262970.9515.9015.51-8.79857809790.51 5.91537096220.815.6015.06-14.77052573830.36 9.24324836160.8215.6414.94-20.98385393740.2 2.98277811130.9715.9415.23-21.52858919380.19 3.77031009960.8315.6614.93-22.56601687530.17 10.18474183330.7815.5614.76-25.03161669390.1 4.44624332310.7215.4414.68-23.67525051920.14 2.43662882390.6615.3214.42-29.25211653050 0.06823261450.6915.3814.64-22.78648173440.16 -2.47822959970.6815.3614.47-28.88616252260.01 -1.51012666160.5415.0814.09-32.9612117723-0.09 -1.81491986420.4814.9613.93-34.3974272411-0.13 -7.55879956290.7215.4414.51-30.4727064003-0.03 -9.75764148640.7215.4414.54-29.28630574490 &"Helvetica Neue,Regular"&12&K000000&P Dataset 5 -13.4086660388 32.2378969633Assignment : Hypothesis Testing 0.9 29Dataset 5136 0.10.075 4.3076696831 63AdditiveYield -5.2258378460.381357117768.72129.519.49113139650.5 0.10.384849411468.77129.469.07701854720.49 63.10.217400934566.26129.264.8822628840.4 3.99897566180.238546321766.58129.8411.20499749170.54 4.15838686550.215584971666.23129.052.44057984140.35 -3.4850605840.134031910165.01128.84-0.82628139840.28 -2.51984633730.331915354467.98127.84-8.91714348060.1 -3.56795304930.536086273971.04127.18-13.40866603880 -7.29057001090.461675332769.93127.74-8.29730507880.11 1.74212909670.638077800172.57128.40.62892516180.31 11.06182983590.838266495575.57128.827.41519665170.46 7.6652261235178128.212.82606314660.36 15.71739246560.800547777275.01129.2111.12275503580.54 24.8553183590.65223749972.78128.784.7881789390.4 32.2378969633 23.1335885096 16.3637340496 &"Helvetica Neue,Regular"&12&K000000&P Dataset 6 Assignment : Hypothesis Testing 15Dataset 6 0.12 G1G2G3 A92411 B151719 SchoolC252318 D161415 E18812 -1.385860928 8.1805382660.98.1393841031.8722507905 9.5663991943.82646785144.59225950645.4262499288 8.1805382667.32761718763.4120823108 3.97345656963.22959334171.0266598779 4.8860731301-1.3858609280.3505985788 1.8722507905 -3.3815906648 -0.0280679988 &"Helvetica Neue,Regular"&12&K000000&P Reference 3 876 Student numbersLast3Seed value B0014235335310.9 B000983733731 B001019679670 B001435825821 B00147010101 B001468378371 B001406626621 B001485725721 B001466546541 B001454394391 B001466276271 B001463093091 B001377707701 B001414644641 B001451101101 B00140024241 B001028528521 B00147030301 B001423003001 B001444634631 B001433073071 B00141010101 B001465345341 B001491121121 B001349699690 B001205855851 B001444484481 B001464554551 B001432192191 B001426106101 B001367657651 B001363223221 B001464794791 B001458768760 B00146051511 B001279159150 B001466886881 B001388828820 B00132032321 B001429569560 B001419019010 B001386406401 B00141067671 B001444144141 B001399759750 B001362762761 B00144085851 B001425035031 B001407247241 B00134039391 B00142018181 B001404304301 B001448638631 B001421981981 B001424584581 B001418788780 B001411111111 B00137073731 B001461761761 B001353113111 B001455025021 B001481461461 &"Helvetica Neue,Regular"&12&K000000&P Statistics and Probability Summer Assignment on Hypothesis Testing May 31, 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 be annotated or explained. 2. It is up to you how you do the calculations in each question, but you must explain how you arrived at your answer for any given calculation. This can be done with a written explanation and by 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 carry 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. Carry 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 carrying out the test will influence the structure of your test. 3. Carry 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 carry- ing out the test would influence the structure of your test. 3. Carry 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 corresponding 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. Carry out the statistical test and state your conclusions. Question 4 A study was carried out to determine whether the resistance of the control circuits in a machine are lower when the machine motor is Page 4 running. 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. Carry out the statistical test and state your conclusions. Question 5 A study was carried 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 corresponding 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 correlation coefficient for the paired data values. 4. Set up the framework for an appropriate statistical test to estab- lish if there is a correlation between the amount of the trace ele- ment and the yield. Explain how having the scatterplot referred to above and having the value of r in advance will influence the structure of your statistical test. 5. Carry out and state the conclusion of your test on the correlation. 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. Carry out this test, showing clearly in your work how the expected values are calculated for your test statistic. Page 6

Aug 21, 2023

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