Moravian College



Statistical Analysis of Weights of M&Ms Name Date of Experiment Date Report Submitted This page, Page 1, is your cover sheet.In what follows, the BLACK text is text you can keep or modify as you wish.The GREEN text contains instructions for you to follow in completing the report. There are tables where you must enter data. Feel free to change the length of the tables to accommodate all the data that you have. I’m sure that you will need to lengthen Table 1.The ORANGE text simulates text you need to write. Replace the orange with your own words. The YELLOW background indicates a place where you must enter numerical results into the text.REMOVE all the colors when you are done!AbstractOur investigation of plain and peanut M&Ms revealed that plain M&Ms have an average mass of xxxx±xxxx g and peanut M&Ms have an average mass of xxxx±xxxx g. Means testing and variance testing showed that plain and peanut M&Ms have significantly different means and standard deviations. A Gaussian distribution function for masses of both types of M&Ms was derived from the data. A hypothesis for the difference in means and standard deviations is suggested.ENTER MEANS AND 95% CONFIDENCE LIMITS IN THE ABSTRACT!IntroductionThe purpose of this experiment is to determine whether plain and peanut M&Ms have significantly different average masses, and have different dispersions in their mass distribution. The t test is used to test the significance of differences in means of experimental data, and the F test is used to test the significance of differences in standard deviation, which measures the dispersion of the populations. The choice of t test depends on the results of the F test.From the mean and standard deviation it is possible to model the distribution of masses as a Gaussian function, the well-known bell-shaped curve. The mean fixes the center (or top) of the curve, and the standard deviation determines the width of the curve—the distance between the inflection points on the curve is the twice the standard deviation. Because the area under the entire curve must equal one (because total probability must equal one), the Gaussian curve is will be tall when it is skinny (small standard deviation) and will be short when it is fat (large standard deviation).Experimental MethodA bag of roughly twenty M&M candies, either plain or peanut, was given to us by the instructor. The mass and color of each M&M candy was recorded; the mass was recorded to 0.1 mg. The M&M data was inserted into a Microsoft Excel file for data analysis, sorted by plain or peanut, and the descriptive statistics tool of each set were calculated: mean, median, standard deviation, minimum, maximum, range, standard error, and 95% confidence limits. F tests and t tests were performed to compare the different sets of M&Ms from different students. The F test was performed to determine whether the subsequent t test had to assume equal or unequal variances. Our goal was to test the statistical significance of difference in the average mass of plain vs peanut M&Ms, but we also performed tests between sets of plain vs plain and peanut vs peanut as control experiments. We expect the control experiments to yield no significant difference between the same type of M&Ms.The entire class’s data was pooled to determine class-wide average masses for the plain and peanut M&M’s, and overall standard deviations. These mean and standard deviations were used to create Gaussian distributions for each set.The mathematical formula for the Gaussian functions isINSERT FORMULA HERE! Lower case s is the symbol for standard deviation.The formula for 95% confidence limits isINSERT FORMULA HERE!Raw DataTable 1 summarizes the raw data I collected for this analysis.Table 1. Plain or Peanut M&M DatacolormassONCE YOU HAVE THE DATA IN THE TABLE, MAKE IT AS NARROW AS POSSIBLE!DO THAT FOR ALL THE TABLES!Data AnalysisDescriptive statistics for each set computed using Excel Table 2. Descriptive Statistics for Plain or Peanut M&Mmeansminmax95% conf limitSignificance TestingData was pooled for comparison among the various sets of M&Ms. Table 3 presents the probabilities produced by the F tests and t test for my set of M&Ms vs others sets of plain M&Ms. Table 3. My Plain or Peanut vs Plain M&M data analysis.plainpeanutP-value (F test)P-value (t test)WHOWHO0.020.001 2?1equal variance t test (type 2 in Excel)2 unequal variance test t (type 3 in Excel) WHICH t TEST DID YOU USE! FOOTNOTE EACH ONE!ENTER STUDENT’S NAMES! FIRST NAME IS ENOUGH!DISCUSS THE RESULTS AND DRAW CONCLUSIONS, BUT ONLY FOR THE RESULTS ABOVE in table 3… that the difference in mean between my which ones M&M data versus the plain data from Jess and Derrick are in/significant. I would expect to obtain a significant or insignificant difference between my Plain or Peanut M&M and plain M&M because…Table 4 presents the probability results of F test and t tests for my set of M&Ms vs. peanut M&Ms. Table 4. My Plain or Peanut vs Peanut M&M data analysis.plainplainP-value (F test)P-value (t test)WHOWHO1 or 2?1equal variance 2 unequal varianceDISCUSS THE RESULTS AND DRAW CONCLUSIONS! ONLY FOR THE RESULTS ABOVE in table 4… that the difference in mean between my which ones M&M data versus the plain data from George and Mary are in/significant. I would expect to obtain a significant or insignificant difference between my Plain or Peanut M&M and peanut M&M because…. Given that a peanut has a considerable mass I would expect the peanut to add a significant mass to the overall mass of the M&M. The data in Table 3 or 4 supports this ideaDistribution FunctionsAll data was pooled to create a large sample from which statistics were computed for plain and peanut M&Ms.The mean value and standard deviation were inserted into Excel's NORMDIST function to create a Gaussian distribution that models the distribution of the masses of the plain M&Ms.Table 5. Class-wide statistics for plain and peanut M&Ms.Mean (g)s (g)plainpeanutFrom these statistics Gaussian distributions can be created for both plain and peanut M&M's. These two distribution functions are plotted in Fig 1.INSERT EXCEL GRAPH HERE USING NORMDIST FOR BOTH!ONLY ONE GRAPH THAT HAS BOTH FUNCTIONS! FUNCTIONS--- THAT MEANS NO MARKERS, JUST LINES!Figure 1. Gaussian distribution of plain and peanut M&Ms derived from the class-wide data.NOTICE THE CAPTION IS UNDER THE FIGURE!Error AnalysisThe F tests revealed that there is no significant difference in the variance values of the M&M masses. However, the F test revealed that there is a significant difference in the variances of the …. HERES WHERE YOU COMPARE ALL THE RESULTS FOR ALL TABLES 3 & 4 ABOVE! WHEN WERE THE DIFFS SIGNIFICANT, AND WHEN Weren’t THEY!ConclusionsThe variance in the masses of plain M&Ms is small in comparison to the variance in the masses of the peanut M&Ms. As seen in the Gaussian curves in Figure …WHAT DOES THE FIGURE TELL YOU!One explanation for the mass difference of the peanut M&Ms is that the mass of the whole peanut … HERE”S WHERE YOU EXPLAIN WHY THE RESULTS CAME OUT THE WAY THEY DID AND PROPOSE YOUR WORLD-SHAKING HYPOTHESIS PROMISED IN THE ABSTRACT!… assume they have the same chocolate composition.Literature CitedHarris,D,C.(2003). Quantitative Chemical.Analysis (6th Ed), p72-74, New York: W. H. Freeman Company.List any reference to the procedure that you followed.Cite a reference other than Harris for the statistical tests.Where did you get any other information you used? ................
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