The Statistical Data from M&M Investigation - Essay Example

M&M Project report Introduction. As a quality control manager at Masterfoods plant, I wrote this report containing all the five parts of M&M project. The first part of the paper discusses the sampling method I used in the research. I bought three M&M bags and recorded the samples in an excel worksheet. The second part is the calculation of sample proportions for each bin: mean of candies, creating the Histogram, compute descriptive statistics, and later summarized the information (Larson & Farber 96). The third part, I located confidence interval of 95% for the total candies in the bin. The fourth part is tested analysis for each bin’s percentage. The last part is the quality control where testing if the ratio of candies in each bin are equal. The paper discusses methods, analysis and results of each part of the project (Larson & Farber 37). The report presents the statistical data from M&M investigation. Additionally, the paper contains mean of candies found in each bag. Testing was conducted to ensure that the set proportions are on target. Consequently, hypotheses were done to ascertain that the proportions are also on target. Part 1. I collected three M&M 1.69 Oz PLAIN M&M candy bag. We counted each color of the candy bag and recorded the total information on a worksheet. The personal samples for the researchers were combined to come up with complete random samples. Each researcher purchased a 1.69Oz bag of plain M&M candy from different shops (Larson & Farber 66). The random sampling method used was to make sure each bag had an equal chance of being selected. Buying the 1.69Oz bags of plain M&M candy ensured a true sample of the bags. After buying the bags were emptied and the number of each candy color was recorded. The results were tabulated as one, in a worksheet. Part2. In this section of the project report, I calculated the proportion of samples for each product color. Additionally, I calculated the mean number of 69Oz bags of plain M&M candies (Larson & Farber 74). I created a Histogram for the candies per bag and summarized the number of calculating proportion. I also calculated the sample SD. Histogram’s explanation was also provided. Sample proportions: I sampled 343 candies. Their proportions based on color were as shown below. Color Number Proportion Blue 79 0.23 Orange 75 0.22 Green 58 0.17 Yellow 41 0.12 Red 45 0.13 Brown 45 0.13 Total 343   Blue: 79, Orange: 75, Green: 58, Yellow: 41, Red: 45, and Brown: 45 Table: Bin Midpoint (x) Frequency (f) fx x^2 F (x^2) 1-2 1.5 5 7.5 2.25 11.25 3-4 3.5 25 87.5 12.25 306.25 5-6 5.5 27 148.5 30.25 816.75 7-8 7.5 46 345.0 56.25 2587.50 9-10 9.5 54 513.0 90.25 4873.50 11-12 11.5 63 724.5 132.25 8331.75 13-14 13.5 27 364.5 182.25 4920.75 15-16 15.5 23 356.5 240.25 5525.75 17-18 17.5 11 192.5 306.25 3368.75 19-20 19.5 4 78.0 380.25 1521.00 21-22 21.5 4 86.0 462.25 1849.00 23-24 23.5 0 0.0 552.25 0.00 25-26 25.5 3 76.5 650.25 1950.75 27-28 27.5 8 220.0 756.25 6050.00 29-30 29.5 3 88.5 870.25 2610.75 31-32 31.5 0 0.0 992.25 0.00 33-34 33.5 3 100.5 1122.25 3366.75 35-36 35.5 6 213.0 1260.25 7561.50 37-38 37.5 3 112.5 1406.25 4218.75 39-40 39.5 7 276.5 1560.25 10921.75 41-42 41.5 9 373.5 1722.25 15500.25 43-44 43.5 8 348.0 1892.25 15138.00 45-46 45.5 4 182.0 2070.25 8281.00 Total 41.5 343 4894.5 1722.25 109711.75 Mean (4894.5/343) 14 Estimated Mean (109711.75/343) 319.8593294 Variance (319.8593-14^2) 123.8593294 SD Sqrt (Variance) 11.12921064 Part 3: I constructed a confidence level of 95% for the proportion of all colors. Additionally, I constructed the means’ confidence level. I also calculated the smallest sample size needed to calculate the confidence interval of 95% for blue candies having a margin error of 4% (Larson & Farber 73). Using the Confidence interval Science calculator at the link http://www.mccallum-layton.co.uk/stats/ConfidenceIntervalCalc.aspx. I found the following results. Blue: (0.21, 0.24), Orange: (0.20, 0.23), Green: (0.15, 0.18), Yellow: (0.12, 0.14), Red: (0.12, 0.14), Brown: (0.12, 0.145) Mean: (13.52, 14). Part 4: I tested the distribution of color in the candies. The following results were noted. Color Hypothesis1(Claim) Hypothesis2 z Decision Comment Evidence Blue 0.24 ≠ 0.2 -2.36 Reject True proportion is not 0.24 Sufficient Orange 0.20 ≠ 0.20 2.75 Reject True proportion is not 0.20 Sufficient Green 0.16 ≠ 0.16 1.07 Fail to reject True proportion is not 0.16 Insufficient Yellow 0.14 ≠ 0.14 -1.57 Fail to reject True proportion is not 0.14 Insufficient Red 0.13 =0.13 -0.1041 Fail to reject True proportion is not 0.13 Insufficient Brown 0.13 =0.13 0.19 Fail to reject True proportion is not 0.13 Insufficient Mean ≤12 >12 .0000 Reject Will contain more than 12 candles Sufficient H0 H1 X2test X2crit Decision Comment Bonus ≥ 1.5 < 1.5 155 47.45 Fail to reject At 5% significance level Evidence is not enough to support SD claim. Part 5: I tested the hypothesis the proportion of red and brown if their population is equal. H0 Ha X1 N1 P1 X2 N2 P2 P-bar z Zcrit (Rejected region) Decision Comment P1=p2 P1≠p2 45 343 0.13 45 343 0.13 .13 -0.21 -1.96 & 1.96 |z| > 1.96 Fail to reject the null No evidence to reject the claim Quality control I investigated if some of the color were off the target. I ascertained the plants setting to make sure no alterations were made. Any anomalies in the mixing or bagging is realized, it may cause variations in their proportion (Larson & Farber 75). During the bagging process, M&M is prone to spill. Consequently, the plant may stop working. Therefore, the machine may need service or replacement. I would recommend for constant service of the machine, in order for the company its set standards. Conclusion. My investigation was a success. The average number of candies was greater than 13. The proportion of colors is on target. The Histogram gave me an easier understanding of the results. The analyses have enabled me to learn that the proportion of M&M is on target. Reference Larson, R., & Farber, B. Elementary statistics. Picturing the world. 4th ed.: N J: 2009. Print. Read More