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Purpose
The purpose of this project is to assess your ability to:
Collect and display data.
Use Excel.
Calculate and interpret expected value.
Calculate the mean, media, and mode of data sets.
Determine whether data sets are normally distributed.
Apply the Central Limit Theorem.
Summarize and report findings.
Overview
This module you will turn in the third part of Project 2. This project consists of three parts.
Project 2-1: Identify the Distribution of a Sample – due in Module 9
Project 2-2: Find A Sampling Distribution of Sample Means – due in Module 10
Project 2-3: Final Submission – due in Module 11
Data that follows a normal distribution pattern is predictable and can be used to draw conclusions. However, many data sets do not follow a normal distribution pattern, and a small sample may not follow the normal distribution even if it comes from a normally distributed population. The Central Limit Theorem tells us that the distribution of sample means will not only be normally distributed, but also, if we have enough samples, the sampling distribution will have a mean that is approximately the same as 𝜇, and a standard deviation that is close to 𝜎𝑛.
To see this, let’s continue the experiment using sets of randomly generated integers.
Action Items
Open your saved Excel file as submitted for Part 2.
Review your gradebook feedback and make any required corrections to Parts 1 or 2.
Complete the tab labeled “Part 3 – Calculate” by using Excel formulas to do the following:Calculate the mean and standard deviation for each of the 4 data sets from Parts 1 and 2.
Calculate the expected standard deviation of the sampling distribution of the sample means.Note, you may either calculate these directly on this tab using cell references, or calculate these using formulas on your original sheets and copy/paste the values into the designated area of the calculation sheet.
Explain how your graphs tables and calculations of the mean and standard deviations relate to the Central Limit Theorem.
View the Project 2 Final Report Example.Download Project 2 Final Report Example.
Download and complete the Probability Project 2-3 – Final Report.Download Probability Project 2-3 – Final Report.
Submit the completed first draft of your assignment. Your work will automatically be checked by Turnitin. Access your Turnitin report by reviewing your Submission Details for this assignment. Revise your work as needed based on the feedback. By the due date indicated, re-submit the final version of your work containing your Final Report and the completed Excel file containing your data and graphs. Note: These items should be submitted at the same time. (If they are submitted separately, any subsequent uploads may override the first submission.)
Rubric
Project 2
Project 2
CriteriaRatingsPts
This criterion is linked to a Learning OutcomePart 1: Random generation of 100 integersGenerate 100 integers randomly using =INT(RAND()*(10)).
Count the frequencies using =countif( and verify the frequency table.
Create a table consisting of expected frequencies and sample(actual) frequencies.
Create a bar chart of the actual frequencies.
Create the expected frequencies (uniform) graph.
5 to >4.0 ptsOne hundred integers were randomly generated correctly using formulas in Excel. The frequencies of each integer (both expected and actual (sample)) are correctly represented in the frequency table. The bar charts of frequencies (both expected and actual (sample)) are accurate. The bar charts have an appropriate title and the axis labels and the x-axis are correct. Improvements were made based on feedback, if applicable.
4 to >2.0 ptsOne hundred (or fewer) integers were randomly generated using formulas in Excel. The frequencies of each integer may not be correctly represented in the frequency table. The bar chart of frequencies may not be accurate. The bar chart may contain errors within the title, axis labels and/or the x-axis. The expected (uniform) bar chart may contain errors. Some improvements may have been made based on feedback.
2 to >0 ptsNo integers were randomly generated or there are major errors in the generation affecting the bar chart and frequency tables. The bar chart, the expected (uniform) graph or frequency table may be missing. Little to no improvements were made based on feedback.
5 pts
This criterion is linked to a Learning OutcomePart 1: Random generation of 1000 integersGenerate 100 integers randomly using =INT(RAND()*(10)).
Count the frequencies using =countif( and verify the frequency table.
Create a bar chart of the actual frequencies.
Create the expected uniform graph.
4 to >3.0 ptsOne thousand integers were randomly generated correctly using formulas in Excel. The frequencies of each integer (both expected and actual (sample)) are correctly represented in the frequency table. The bar charts of frequencies (both expected and actual (sample)) are accurate. The bar charts have an appropriate title and the axis labels and the x-axis are correct. Improvements were made based on feedback, if applicable.
3 to >1.0 ptsOne thousand (or fewer) integers were randomly generated using formulas in Excel. The frequencies of each integer may not be correctly represented in the frequency table. The bar chart of frequencies may not be accurate. The bar chart may contain errors within the title, axis labels and/or the x-axis. Some improvements may have been made based on feedback.
1 to >0 ptsNo integers were randomly generated or there are major errors in the generation affecting the bar chart and frequency tables. The bar chart or frequency table may be missing. Little to no improvements were made based on feedback.
4 pts
This criterion is linked to a Learning OutcomePart 1: AnalysesWrite two paragraphs comparing
the expected uniform graph to the bar chart of frequencies (n=100) and comparing the graphs of n=1000 to the graphs of n=100.
5 to >4.0 ptsThe analysis for the n=100 case is thorough and accurate. It compares and contrasts the expected uniform graph with the bar chart of actual frequencies. The analysis addresses if the same indicates a uniform distribution. The analysis for n=1000 compares and contrasts the graphs of both cases (n=100 & n=1000). Two additional observations are made. Improvements were made based on feedback, if applicable.
4 to >2.0 ptsThe analysis for both cases is present. There are some errors in the comparisons. Some improvements may have been made based on feedback.
2 to >0 ptsThere are no analysis paragraphs, or one of them is missing. If both are present, there are major errors in both of them. Little to no improvements were made based on feedback.
5 pts
This criterion is linked to a Learning OutcomePart 2: Distribution of Sample Mean n=4Create a data set consisting of 250 samples of size n=4.
Calculate the mean of each sample set of 4 values by using =average(.
Verify the counts in the frequency table by using =countif.
4 to >3.0 ptsThe data set is correct. The mean is correct for each sample set. The frequency table was verified. Improvements were made based on feedback, if applicable.
3 to >1.0 ptsThe data set and means are present, but there are errors with some of them. The frequency table may not have been verified. Some improvements may have been made based on feedback.
1 to >0 ptsThe data set was not created, the means were not calculated, nor was the frequency table verified. If the required parts are present, they contain major errors. Little to no improvements were made based on feedback.
4 pts
This criterion is linked to a Learning OutcomePart 2: Distribution of Sample Mean n=16Create a data set consisting of 1000 samples of size n=16.
Calculate the mean of each sample set of 16 values by using =average(.
Verify the counts in the frequency table by using =countif.
4 to >3.0 ptsThe data set is correct. The mean is correct for each sample set. The frequency table was verified. Improvements were made based on feedback, if applicable.
3 to >1.0 ptsThe data set and means are present, but there are errors with some of them. The frequency table may not have been verified. Some improvements may have been made based on feedback.
1 to >0 ptsThe data set was not created, the means were not calculated, nor was the frequency table verified. If the required parts are present, they contain major errors. Little to no improvements were made based on feedback.
4 pts
This criterion is linked to a Learning OutcomePart 2: Analyses of the DistributionsWrite two paragraphs.
For n=4: compare the graph to previous distributions using at least two observations.
For n= 16: compare the graph to previous distributions using at least two additional observations.
4 to >3.0 ptsMeets Expectations
The analyses for both distributions contain the appropriate comparisons including observations. The information is correct and concise. Improvements were made based on feedback, if applicable.
3 to >1.0 ptsThe analysis for both cases is present. There are some errors in the comparisons. Some improvements may have been made based on feedback.
1 to >0 ptsThere are no analysis paragraphs, or one of them is missing. If both are present, there are major errors in both of them. Little to no improvements were made based on feedback.
4 pts
This criterion is linked to a Learning OutcomePart 3: Mean and Standard DeviationCalculate the mean and standard deviation for of the four data sets in Parts 1 and 2.
6 to >5.0 ptsThe means and standard deviations are all calculated and are correct.
5 to >1.0 ptsThe means and standard deviations are all calculated, but contain some errors.
1 to >0 ptsThe means and standard deviations are not calculated, or if they are there are major errors.
6 pts
This criterion is linked to a Learning OutcomePart 3: Expected Standard DeviationCalculate the expected standard deviation of the sampling distribution of the sample means.
3 to >2.0 ptsThe expected standard deviation of the sampling distribution of the sample means is calculated and is correct.
2 to >1.0 ptsThe expected standard deviation of the sampling distribution of the sample means is calculated but is incorrect.
1 to >0 ptsThe expected standard deviation of the sampling distribution of the sample means is not calculated.
3 pts
This criterion is linked to a Learning OutcomePart 3: AnalysisExplain how the graphs, tables and calculations of the mean and standard deviations relate to the Central Limit Theorem.
5 to >4.0 ptsThe analysis includes an in-depth explanation of how the findings related to the Central Limit Theorem. The analysis is thorough and succinct.
4 to >2.0 ptsThe analysis is included, but does not clearly relate the findings to the Central Limit Theorem. The analysis is not thorough and succinct.
2 to >0 ptsThe analysis is not included or if it is, it contains major gaps.
5 pts
This criterion is linked to a Learning OutcomePart 4: IntroductionWrite a brief overview of the purpose of this experiment and what the reader should expect to learn from this report.
3 to >2.0 ptsAn introduction is included. It describes the project and what a reader can expect to learn.
2 to >1.0 ptsAn introduction is included but it does not describe the project or does not describe what a reader can expect to learn.
1 to >0 ptsAn introduction is not included or if included, it contains major gaps.
3 pts
This criterion is linked to a Learning OutcomePart 4: Excel WorkbookFile is complete and submitted.
2 ptsThe Excel file is complete and contains all of the correct information.
1 ptsThe Excel file may not may not be complete or may be complete but has inaccuracies.
0 ptsThe Excel file was not submitted.
2 pts
This criterion is linked to a Learning OutcomePart 4: Graphs and TablesInclude copies of all tables and charts in the report. See the sample report for reference.
2 ptsAll tables and charts are included in the report.
1 ptsSome tables and charts are missing.
0 ptsThe tables and charts were not included in the report.
2 pts
This criterion is linked to a Learning OutcomePart 4: Mechanics
3 to >2.0 ptsBoth report and Excel workbook submitted. Report contains no grammatical or formatting errors.
2 to >1.0 ptsEither report or Excel workbook not submitted. Report contains some grammatical or formatting errors.
1 to >0 ptsReport and/or Excel workbook not submitted. Report contains major grammatical or formatting errors.
3 pts
Total Points: 50
attatched is a sample of what it should look like and also a outline to add answers. thanks so much in advance