5 Pages

# M&M Final Project_Statistics

Course Number: MAT 300, Spring 2013

College/University: Strayer

Word Count: 368

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Running head: M&M PROJECT REPORT M&M Project Report Erla Reyes Course: Mat-300 Professor: Daniel Burnell Date: June 20, 2013 Strayer University Online M&M PROJECT REPORT 2 Project Part 1: Sampling Method there are four methods of sampling available. The following are defined as follow: 1: Simple Random Sampling In this method, individuals are randomly selected from a list of the population and...

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head: Running M&M PROJECT REPORT M&M Project Report Erla Reyes Course: Mat-300 Professor: Daniel Burnell Date: June 20, 2013 Strayer University Online M&M PROJECT REPORT 2 Project Part 1: Sampling Method there are four methods of sampling available. The following are defined as follow: 1: Simple Random Sampling In this method, individuals are randomly selected from a list of the population and every single individual has an equal chance of selection. 2) Systematic Sampling When using systematic sampling, every key element from the list is selected (this is referred to as the sample interval) from a randomly selected starting point. For example, if we have a listed population of 40 members and wish to draw a sample of 10, we would select every 4th (40 divided by 10) person from the list. In practice, we would randomly select a number between 1 and 4 to act as our starting point. 3) Stratified Sampling this method is used when there are a number of distinct subgroups, within each of which it is required that there is full representation. A stratified sample is constructed by classifying the population in sub-populations, based on some distinguished characteristics of the population, such as age, gender or socio-economic status. 4) Cluster Sampling This is largely done by first sampling at the higher level(s) e.g. randomly sampled countries, then sampling from subsequent levels in turn e.g. within the selected countries sample counties, then M&M PROJECT REPORT 3 within these postcodes, the within these households, until the final stage is reached, at which point the sampling is done in a simple random manner e.g. sampling people within the selected households. The 'levels' in question are defined by subgroups into which it is appropriate to subdivide your population. At M&M we use Simple Random Sampling method to get the data. Project Part 2: Method, Analysis, Results Method: Descriptive Statistics The following is a randomly selected data. Blue Orange Green Yellow Red Brown 987 951 774 578 550 527 Total of Number Candies in 78 bags 4362 4362 4362 4362 4362 4362 Mean=55.92 and Standard Deviation=3.29 Analysis and Results: From the above data, the conclusion is that, on average in a single bag we have 56 candies and with a variation of 4 candies. The following table shows the details of color proportion in each bag. Color Blue Orange Green Yellow Red Brown Percentage of candies in a bag 22% 22% 18% 13% 13% 12% Candies in a bag 13 13 10 7 7 6 M&M PROJECT REPORT 4 Project Part 3: Method, Analysis, Results Method: Confidence Intervals for a Population Proportion. Analysis and Results: The following is a constructing 95% Confidence Interval for the every color proportion. And results are as follows: Color Confidence Interval Percentage of candies per bag at 95% CI Blue 0.2139, 0.2387 21.39% to 23.87% Orange 0.2057, 0.2303 20.57% to 23.03% Green 0.1661, 0.1887 16.61% to 18.87% Yellow 0.1224, 0.1426 12.24% to 14.26% Red 0.1162, 0.1360 11.62% to 13.60% brown 0.1111, 0.1305 11.11% to 13.05% * Candies per bag to construct a 95% confidence interval Candies * 12 14 12 13 9 11 78 68 6-7 Project Part 4: Method, Analysis, Results Method: Hypothesis Test for Proportions Analysis and Results The Hypothesis test was applied at 0.05 significance level and found that test is failed for the Brown, Yellow, and Red Color candies, it could be possible to a lack production, capacity, or even assortment. Project Part 5: Method, Analysis, Results Method: Two-Sample z-Test for the difference between proportions. Analysis and Results: In this we have to test that the population proportions of red and brown are equal (pred = pbrown). 1: Hypotheses H0: pred = pbrown Ha: predpbrown M&M PROJECT REPORT 5 2: Test statistic p^red-p^brown = 0.0053 3: Critical values -1.96 , 1.96 4: Z (standardized test statistic) Z=0.7486 5: Decision Fail to reject. References Larson, R., & Farber, B. (2009). Retrieved from Elementary Statistics Picturing the World: 2009 custom edition (4th ed.). NJ: Pearson Custom Publishing.

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