Probability and Statistics Competency Demonstration Project

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timer Asked: Jul 1st, 2018
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Please see the attached pdf file for instructions. I am also including a guide to use microsoft excel for the project. Thank you in advance for all of your help!

MATH 106 Statistics Project Instructions Version 2.1 (Summer 2016) MATH 106 Statistics Project Instructions (Revised May 2016) For this assignment, you will implement a project involving statistical procedures. The topic may be something that is related to your work, a hobby, or something you found interesting. If you choose, you may use the example described below. The project is made of the following tasks. Each task must be addressed in the statistics project report in order to qualify for full credit:        Task 1: identify: o Yourself (student’s name) o name of project o purpose of project Task 2: Conduct Data Collection. Provide: o Raw data used (sample size must be at least 10 individual raw scores) o source of the data Task 3: Calculate Measures of Central Tendency and Variability: o median, sample mean, range, sample variance, and sample standard deviation (show work) Task 4: Frequency Distribution. Provide o Raw data in frequency table format (1st column of value “intervals”, and 2nd column shows “frequency”: number of scores falling within each interval) Task 5: Histogram: o Create histogram using frequency table constructed in Task 4 o NOT a vertical bar chart! o x – axis must show intervals, y – axis must show frequencies Task 6: Compare Raw Data Distribution to “Standard” Normal Distribution. Using your raw data gathered in Task 2 and the sample mean and sample standard deviation calculated in Task 3, calculate: o percentage of your raw data falling within one standard deviation of the mean; o percentage of your raw data falling within two standard deviations of the mean; o percentage of your raw data falling within three standard deviations of the mean Task 7: Communicating Evaluation, Analysis, Results, and Conclusions. Provide two to three paragraphs that: o interpret your statistics and graphs; o answer whether your percentages calculated in Task 6 indicate that your data distribution (shown in the histogram created in Task 5) is the same as the 68/95/99.5% “standard” normal distribution? Be sure to explain why you think your data distribution does or does not match the “standard” normal distribution. o relate to the purpose of the project 1 MATH 106 Statistics Project Instructions Version 2.1 (Summer 2016) ***************************************************************************** If you choose, you may use the following example for your data.  Purpose: Compare the amount of sugar in a standard serving size of different brands of cereal. (You may instead choose to compare the amount of fat, protein, salt, or any other category in cereal or some other food.)  Procedure: Go to the grocery store (or your pantry) and pick at least 10 different brands of cereal. (Instead of choosing a random sample, you might purposely pick from both the "healthy" cereal types and the "sugary" ones.) From the cereal box, record the suggested serving size and the amount of sugar per serving. The raw data is the serving size and amount of sugar per serving for each of the 10 boxes of cereal. Before calculating the statistics on the amount of sugar in each cereal, be sure you are comparing the same serving size. If you use a serving size of 50 grams, you must calculate how much sugar is in 50 grams of each cereal. For example, if the box states that there are 9 grams of sugar in 43 grams of cereal, there would be 50 times 9 divided by 43, or 10.5 grams in 50 grams of cereal. The result of this simple calculation (for each of 10 boxes) is the data you will use in the project statistics and charts. ****************************************************************************** For Task 6: Instructions for Calculating Percentage of Raw Data Falling Within 1, 2, and 3 Standard Deviations of Mean: 1. Determine sample mean 𝑥̅ and sample standard deviation s for your raw data set (you had to do this to complete Task 3 so they should already be done) 2. Determine the raw score “bounds” for data falling within 1 standard deviation of the mean by subtracting 1 standard deviation from the mean to get the lower bound. Then, add 1 standard deviation to the mean to get the upper bound. 3. Count the number of raw scores in your data set whose values fall between the lower and upper bounds you found in Step 2. Divide that number by n, the total number of scores in your data set, and then multiply the result by 100 to get the percent of raw data falling within one standard deviation of the mean. 4. Now, determine the raw score “bounds” for data falling within 2 standard deviations of the mean by subtracting 2 standard deviations from the mean to get the lower bound. Then, add 2 standard deviations to the mean to get the upper bound. 5. Count the number of raw scores in your data set whose values fall between the lower and upper bounds you found in Step 4. Divide that number by n, the total number of scores in your data set, and then multiply the result by 100 to get the percent of raw data falling within 2 standard deviations of the mean. 6. Now, determine the raw score “bounds” for data falling within 3 standard deviations of the mean by subtracting 3 standard deviations from the mean to get the lower bound. Then, add 3 standard deviations to the mean to get the upper bound. 7. Count the number of raw scores in your data set whose values fall between the lower and upper bounds you found in Step 6. Divide that number by n, the total number of scores in your data set, and then multiply the result by 100 to get the percent of raw data falling within 3 standard deviations of the mean. 2 MATH 106 Statistics Project Instructions Version 2.1 (Summer 2016) Example: The following measurements of grams of fat per ¼ - pound serving of 10 different brands of ground beef were made: 17 22 11 26 13 23 15 15 18 30 Calculate the percentage of raw data falling within 1, 2, and 3 standard deviations of the mean: SOLUTION: 1. Determine sample mean 𝑥̅ and sample standard deviation s for your raw data set (you had to do this to complete Task 3 so they should already be done). Sample mean 𝑥̅ = 19.0 and sample standard deviation s = 6.074 2. Determine raw score “bounds” for data falling within 1 standard deviation of the mean: a. subtract 1 standard deviation from mean to get lower bound:  19.0 – 6.074 = 12.926 b. add 1 standard deviation to mean to get upper bound:  19.0 + 6.074 = 25.074 3. Count number of raw scores in your data set whose values fall between 12.926 (lower bound) and 25.074 (upper bound). 7 out of 10 of the raw scores fall between the bounds (“11”, “26”, and “30” fall outside the bounds). Divide 7 by total number of scores in data set n = 10 , and then multiply result 0.7 by 100 to get 70 percent of raw data falling within 1 standard deviation of mean. 4. Now, determine raw score “bounds” for data within 2 standard deviations of the mean: a. subtract 2 standard deviations from mean to get lower bound:  19.0 – (2 x 6.074) = 19.0 – 12.148 = 6.852 b. add 2 standard deviations to mean to get upper bound:  19.0 + (2 x 6.074) = 19.0 + 12.148 = 31.148 5. Count number of raw scores in your data set whose values fall between 6.852 (lower bound) and 31.148 (upper bound). All 10 out of 10 of the raw scores fall between the bounds. Divide 10 by total number of scores in data set n = 10, and then multiply result 1 by 100 to get 100 percent of raw data falling within 2 standard deviations of mean. 6. Now, determine raw score “bounds” for data within 3 standard deviations of the mean: a. subtract 3 standard deviations from mean to get lower bound:  19.0 – (3 x 6.074) = 19.0 – 18.222 = 0.778 b. add 3 standard deviations to mean to get upper bound:  19.0 + (3 x 6.074) = 19.0 + 18.222 = 37.222 7. Count number of raw scores in your data set whose values fall between 0.778 (lower bound) and 37.222 (upper bound). Again, all 10 out of 10 of the raw scores fall between the bounds. Divide 10 by total number of scores in data set n = 10, and then multiply result 1 by 100 to get 100 percent of raw data falling within 3 standard deviations of mean. Now you decide how the raw data distribution of “70/100/100” percent within 1/2/3 std deviations of the mean compares with the “68/95.5/99” percent of the “standard” normal distribution? 3
MATH 106 CBE-ELM V1.0 (Summer 2016) Using MS Excel for MATH 106 Competency Skills Reviews 206/207, the Probability & Statistics Project, and the MATH 106 Comprehensive Competency Assessment (Final Exam) Assuming you know how to enter numbers into an Excel spreadsheet, here are the corresponding functions from Excel that will help you:   Create a histogram (NOT a “bar chart”) to visually display data distribution; and Calculate the statistical measures of central tendency and variability that we cover in MATH 106 Weeks 6 and 7 To create a histogram using Excel 2013 for Windows:         In spreadsheet, enter midpoint values of intervals in Column A Enter corresponding frequencies in Column B Highlight data in both columns Click on "INSERT" pull-down at top of window; chart icons appear in top middle of window. Click on any chart type you wish (I use "Recommended Chart") New window "Insert Chart" appears with your data depicted as a chart. Select "OK" at bottom right of this window. Window with your chart appears. Go to upper left of menu at top of screen and click on "Quick Layout" icon. Small window with 11 chart type images appears (3 rows of 3 columns, 4th row has only 2 columns). The histogram chart type is in the 3rd row from top, in the 2nd column. Click on this image. Window with your chart now displays in histogram form. Add titles/legends/info as desired. Save chart as desired. I regret I don't have a Mac so I can't tell you if the exact same sequence works in Excel 2013 for Mac (but it's probably close!). 1 MATH 106 CBE-ELM V1.0 (Summer 2016) Find measures of central tendency & variability using Excel: If You Want to Find Mean (𝑥̅ ) Median Mode (single) Ungrouped Sample Variance (s2) Ungrouped Sample Standard Deviation (s) Ungrouped Population Variance (σ2) Ungrouped Population Standard Deviation (σ) In Excel 2007 Use Function MEAN MEDIAN MODE VAR.S In Excel 2010 Use Function MEAN MEDIAN MODE.SNGL VAR.S In Excel 2013 Use Function AVERAGE MEDIAN MODE.SNGL VAR.S STDEV.S STDEV.S STDEV.S VAR.P VAR.P VAR.P STDEV.P STDEV.P STDEV.P For example, let’s say 8 students were surveyed about the amount of hours per week they spend working on MATH 106. The individual responses (8, 11, 15, 9, 14, 12, 10, 12) are also listed in the “Scores” column below. From that, follow along to see how the measures of central tendency and variation are found. Measure n= Ungrouped MEAN (𝑥̅ ) = MEDIAN = MODE = Amount 8 11.375 11.5 12 How to Find Using Excel enter total number of scores found using MEAN (Excel 2007,2010) or AVERAGE (Excel 2013) function found using MEDIAN function found using MODE.SNGL function Ungrouped Sample Variance (s2) = 5.696 found by using VAR.S function Ungrouped Sample Standard Deviation (s) = 2.387 found by using STDEV.S function Ungrouped Population Variance (σ2) = 4.984 found by using VAR.P function Ungrouped Population Standard Deviation (σ) = 2.233 found by using STDEV.P function Try it by hand using same scores so you’ll feel confident that Excel can do what you want it to. 2 MATH 106 CBE-ELM V1.0 (Summer 2016) To convert raw scores (x) into z – scores: Excel 2010 / 2013:     Select function "STANDARDIZE". Next, enter raw score (X) you want to convert Next, enter mean (M) Next, enter standard deviation (SD) You get as a result the z-score that corresponds to the raw score you entered Example: for the study we did above, find the z – score equating to raw score of “8”. Solve: From the example above, we know the mean of the data set is 11.375 and the sample standard deviation (STDEV.S) is 2.387 In open spreadsheet cell, enter: =STANDARDIZE(8,11.375,2.387), then hit “return” You get as a result the z-score of – 1.414 corresponds to the raw score of 8 in the example’s data set. 3

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Robert__F
School: University of Maryland

Please let me know if there is anything needs to be changed or added. I will be also appreciated that you can let me know if there is any problem or you have not received the work. Please let me know if there is anything needs to be changed or added. I will be also appreciated that you can let me know if there is any problem or you have not received the work Good luck in your study and if you need any further help in your assignments, please let me know Can you please confirm if you have received the work? Once again, thanks for allowing me to help you R P.S: Studypool is facing high level of traffic which may delay the downloading process....

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