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Words 987

Pages 4

M&Ms® Project

Part 3 (21 pts)

We will be constructing confidence intervals for the proportion of each color as well as the mean number of candies per bag. You will use the methods of 6.3 for the proportions and 6.1 for the mean. For the Bonus, you will use the sample size formula on page 338.

You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found under Tools for Success in Course Home. Here is also a link: http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html. You can also find additional help on both confidence intervals and StatCrunch in the Online Math Workshop under Tab: “MAT300 Archived Workshops”. Specifically you will be looking for Confidence Intervals and Using Technology – CI.

Submit your answers in Excel, Word or pdf format. Submit your file through the M&M® project link in the weekly course content. If calculating by hand, be sure to keep at least 4-6 decimal places for the sample proportions to eliminate large rounding errors.

3 pts. Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of orange M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of green M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of yellow M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of red M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of brown M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the mean total number of candies (large samples).

BONUS: 5 pts. How many candies should be sampled to obtain a 95% CI of the proportion of blue candies with a 4% margin of error if the known proportion of blue candies is 0.24?

HELP:

Color Proportions…...

...started with the project three 1.69 ounce bags of plain M&M’s were purchased from Walgreens, Rite-Aid and Dollar General. These bags will help with taking a sample of the population that is produced. Purchasing the bags from three different stores will help with the results of the project being meaningful because it is assured that the samples will be truly random. Random sampling is when all members of a group have an equal and independent chance of being selected. Next each individual bag of candy was opened and counted. When counting the candies were put into groups based on their color (blue, orange, green, yellow, red and brown) and the results were recorded on a spreadsheet. Once every bag was counted the findings were added up to find the total number of candies within each of the three 1.69 ounce bags of plain M&M’s. The findings were as followed: Bag One had 54 candies, Bag Two had 57 candies and Bag Three had 56 candies. Part 2 For this part of the project all of the data findings from the class were combined into one class data set. The data focused on the color proportions and the number of candies per bag. The information that was used for the color proportions is the total for each color and the total number of candies sampled. The data in the number candies in bag column was used for the number of candies per bag. First the sample proportions for each of the colors were calculated. A sample proportion is the number of individuals in the sample with a......

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...Hypothesis Testing and Confidence Intervals a. The average (mean) annual income was less than $50,000 Null Hypothesis: The average annual income was greater than or equal to $50,000 H₀: µ > 50000 Alternate Hypothesis: The average annual income was less than $50,000. Ha: µ > 50000 Analysis Plan: Significance Level, α=0.05. Since the sample size, n > 30 I will use z-test for mean to test the given hypothesis. As the alternative hypothesis is Ha: µ > 50000, the given test is a one-tailed z-test. Critical Value and Decision Rule: The critical value for significance level, α=0.05 for a lower-tailed z-test is given as-1.645. Decision Rule: Reject H₀, if z – statistic, -1.645 Test Statistic - minitab One-Sample Z: Income ($1000) Test of mu = 50 vs < 50 The assumed standard deviation = 14.55 95% Upper Variable N Mean StDev SE Mean Bound Z P Income ($1000) 50 43.48 14.55 2.06 46.86 -3.17 0.001 Interpretation of Results and Conclusion: Since the P-value (0.0001) is smaller than the significance level (0.05), we reject the null hypothesis. The p-value implies the probability of rejecting a true null hypothesis. The significance level of 0.05, there is enough evidence to support the claim that the average annual income was less than $50,000. Confidence Interval - minitab One-Sample Z The assumed standard deviation = 14.55 N Mean SE Mean 95% CI 50 43.48 2.06 (39.45, 47.51) The 95% upper confidence limit is 47.51. Since,...

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...pts) We will be constructing confidence intervals for the proportion of each color as well as the mean number of candies per bag. You will use the methods of 6.3 for the proportions and 6.1 for the mean. For the Bonus, you will use the sample size formula on page 338. You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found under Tools for Success in Course Home. Here is also a link: http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html. You can also find additional help on both confidence intervals and StatCrunch in the Online Math Workshop under Tab: “MAT300 Archived Workshops”. Specifically you will be looking for Confidence Intervals and Using Technology – CI. Submit your answers in Excel, Word or pdf format. Submit your file through the M&M® project link in the weekly course content. If calculating by hand, be sure to keep at least 4-6 decimal places for the sample proportions to eliminate large rounding errors. 3 pts. Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of orange M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of green M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of yellow M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of red M&Ms® candies. 3 pts. Construct a 95% Confidence......

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...pts) We will be constructing confidence intervals for the proportion of each color as well as the mean number of candies per bag. You will use the methods of 6.3 for the proportions and 6.1 for the mean. For the Bonus, you will use the sample size formula on page 338. You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found under Tools for Success in Course Home. Here is also a link: http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html. You can also find additional help on both confidence intervals and StatCrunch in the Online Math Workshop under Tab: “MAT300 Archived Workshops”. Specifically you will be looking for Confidence Intervals and Using Technology – CI. Submit your answers in Excel, Word or pdf format. Submit your file through the M&M® project link in the weekly course content. If calculating by hand, be sure to keep at least 4-6 decimal places for the sample proportions to eliminate large rounding errors. 3 pts. Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of orange M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of green M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of yellow M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of red M&Ms® candies. 3 pts. Construct a 95% Confidence......

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...A statistical analysis of consumer confidence and unemployment numbers An analysis in R Clemens Timmermans (s0867144) 5/1/2009 INTRODUCTION Statistics matters. CBS.nl presents Dutch facts every month and to make sense of this data statistical analysis is a must. Without this kind of analysis these numbers are just numbers without meaning. For this paper the input came from CBS.nl as well, and here I will outline what the predictive capability of the consumer confidence indicator is for unemployment rates in the Netherlands. There could be a possible causal relationship between customer confidence and unemployment numbers because the consumer confidence indicator is assumed to be an indicator of their buying behavior and therefore may influence employment numbers, because products may or may not have to be produced if customers start or stop buying them. In this paper we will explore the data and see if there is such a causal relationship. Of course, a misinterpretation of numbers due to statistics is a problem that is lurking, and should be taken seriously. Therefore constructing conclusions in a valid way is important and by showing my full line of thought this is how I try to avoid, or at least expose, interpretation errors. The reason that this type of research has value for business is that the knowledge obtained in this paper may be an input into decision making about hiring new employees for instance. Furthermore, it is important to know how long it takes in......

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...estimate of the mean overpayment is simply a good guess about what the average overpayment for the population is. Investigating all 1,000 claims and obtaining the overpayment amount for each would either be impractical, unfeasible or both. Thus, the auditor deems a sample size of 50 claims to be adequate and sufficiently representative of the entire population. The mean overpayment amount of this sample is then calculated in order to obtain a point estimate of the mean overpayment. The estimated mean is then extrapolated to the overpayment amount to the population of all 1,000 claims. http://pages.wustl.edu/montgomery/lecture-7 Point Estimate vs. Interval Estimate To estimate population parameters, statisticians use sample statistics. For example, we use sample means to estimate population means and we use sample proportions to estimate population proportions. An estimate of a population parameter can be expressed in one of two ways: * Point estimate. A point estimate of a population parameter is a single value of a statistic. For example, the sample mean x is a point estimate of the population mean μ. In the same way, a sample proportion p is a point estimate of the population proportion P. * Interval estimate. An interval estimate is defined by two numbers, and the population parameter is said to lie between those two numbers. For example, a < x < b represents an interval estimate of the population mean μ. It expresses that the population mean is......

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...paper is about the color proportion of each bag of M&Ms®. Now even though the factory has a claim of the each bag being grouped off into a certain percentage of each color, the results are not always the same. In fact, I will show through random selection process that M&Ms® brand candies each have a different number of candies in the bag and from that a different percentage of each color represented. I will use different statistical formulas and hypotheses to state my claim and give evidence as it relates to the results of the claim. This study was conducted in 5 different parts, by a total of 74 people, each person obtaining bags of M&Ms® in the same manner but in different locations. Title The purpose of this report is to examine the packaging process for plain 1.69 ounce bags of M&Ms®. . Part 1 For the first part of this project I went to three different stores, (Publix, Piggly Wiggly, and Trinity Gift Shop) and purchased a bag of plain 1.69oz M&Ms® at each store. Purchasing a single bag at a random store assured the process of obtaining a true random sample. After purchasing each bag of M&Ms®, I separated each bag by color and charted the results into an Excel spreadsheet: | Blue | Orange | Green | Yellow | Red | Brown | Num. of Candies in Bag | bag 1 | 2 | 14 | 12 | 8 | 10 | 11 | 57 | bag 2 | 7 | 20 | 7 | 7 | 9 | 9 | 59 | bag 3 | 10 | 4 | 6 | 7 | 16 | 13 | 56 | The data was then combined with 73 other random bags of M&Ms®,......

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...Statistics (GM533) Course Project Case Study: Grocery Bags data gathered and written by ME Applied Managerial Statistics GM533 Instructor: XX I. Executive Summary For this research I decided to develop my own case study and collect all the data myself. The data file named “Grocery Bag Study” (separate attachment), contains observations on 33 sample groups with a variation of 8 different characteristics (see table below). These characteristics include ethnicity, number of adults and minors in household, the number of bags collected weekly, the number of bags they recycle or reuse, the use of reusable fabric shopping bags, how many they throw away and the sex of the adults in the household. The totals for the bags are shown in the table below (Table A.1). For the sake of this study, I am going to combine the paper and plastic together because I want my dependent variable to be the number of bags recycled each week. I want to determine if the independent variables affect the recycle rate and which ones affect it the most, which can be eliminated and what my conclusions will be. II. Calculations This file was used to prepare a report on the influence of various options on grocery bags collected each week and to relay how this information could be used to determine the recycle rates (y). Statistical analysis by Hypothesis Testing and Multiple Regression Analysis was performed on the collection of grocery bags and it was found that there are 5 independent......

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...STAT 121: Writing Assignment 1 Confidence Intervals http://homeworklance.com/downloads/stat-121-writing-assignment-1-confidence-intervals/ STAT 121: Writing Assignment 1 Confidence Intervals Confidence Intervals (12 points) Directions: Read the following article and answer each question completely but concisely. Be sure to save a copy of your work, and see the syllabus for submission details. (The spacing between the questions is not necessarily an indication of the expected response length.) Journal March 26, 2010 Resting Heart Rates of American Adults A normal resting heart rate for adults ranges from 60 to 100 beats a minute,” reports Dr. Edward Laskowski of the Mayo Clinic. Lower resting heart rates are generally associated with higher cardiovascular fitness. With the marked increase in obesity in America, there is rising concern that the average resting heart rate of American adults is trending towards the higher end of the accepted range. A recent study conducted by the Statistical Health Association of America validates this concern. Results were based on a sample of 1587 American adults (ages 18 and older). The mean resting heart rate from this sample was calculated at 87 beats per minute (bpm). The study concludes that, with 95% confidence, the true mean resting heart rate of American adults is in the interval (80, 94). (1 point) What is the population that the confidence interval in the article is making an inference about? Be specific. It is making an......

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...STAT 121: Writing Assignment 1 Confidence Intervals To Buy this Class Copy & paste below link in your Brower http://homeworkregency.com/downloads/stat-121-writing-assignment-1-confidence-intervals/ Or Visit Our Website Visit : http://www.homeworkregency.com Email Us : homeworkregency@gmail.com STAT 121: Writing Assignment 1 Confidence Intervals STAT 121: Writing Assignment 1 Confidence Intervals (12 points) Directions: Read the following article and answer each question completely but concisely. Be sure to save a copy of your work, and see the syllabus for submission details. (The spacing between the questions is not necessarily an indication of the expected response length.) Journal March 26, 2010 Resting Heart Rates of American Adults A normal resting heart rate for adults ranges from 60 to 100 beats a minute,” reports Dr. Edward Laskowski of the Mayo Clinic. Lower resting heart rates are generally associated with higher cardiovascular fitness. With the marked increase in obesity in America, there is rising concern that the average resting heart rate of American adults is trending towards the higher end of the accepted range. A recent study conducted by the Statistical Health Association of America validates this concern. Results were based on a sample of 1587 American adults (ages 18 and older). The mean resting heart rate......

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...pts) We will be constructing confidence intervals for the proportion of each color as well as the mean number of candies per bag. You will use the methods of 6.3 for the proportions and 6.1 for the mean. For the Bonus, you will use the sample size formula on page 338. You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found under Tools for Success in Course Home. Here is also a link: http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html. You can also find additional help on both confidence intervals and StatCrunch in the Online Math Workshop under Tab: “MAT300 Archived Workshops”. Specifically you will be looking for Confidence Intervals and Using Technology – CI. Submit your answers in Excel, Word or pdf format. Submit your file through the M&M® project link in the weekly course content. If calculating by hand, be sure to keep at least 4-6 decimal places for the sample proportions to eliminate large rounding errors. 3 pts. Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of orange M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of green M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of yellow M&Ms® candies. 3 pts. Construct a 95% Confidence Interval for the proportion of red M&Ms® candies. 3 pts. Construct a 95% Confidence......

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...Assignment 1 Confidence Intervals http://homeworkregency.com/downloads/stat-121-writing-assignment-1-confidence-intervals/ STAT 121: Writing Assignment 1 Confidence Intervals (12 points) Directions: Read the following article and answer each question completely but concisely. Be sure to save a copy of your work, and see the syllabus for submission details. (The spacing between the questions is not necessarily an indication of the expected response length.) Journal March 26, 2010 Resting Heart Rates of American Adults A normal resting heart rate for adults ranges from 60 to 100 beats a minute,” reports Dr. Edward Laskowski of the Mayo Clinic. Lower resting heart rates are generally associated with higher cardiovascular fitness. With the marked increase in obesity in America, there is rising concern that the average resting heart rate of American adults is trending towards the higher end of the accepted range. A recent study conducted by the Statistical Health Association of America validates this concern. Results were based on a sample of 1587 American adults (ages 18 and older). The mean resting heart rate from this sample was calculated at 87 beats per minute (bpm). The study concludes that, with 95% confidence, the true mean resting heart rate of American adults is in the interval (80, 94). 1. (1 point) What is the population that the......

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...3 (21 pts) We will be constructing confidence intervals for the proportion of each color as well as the mean number of candies per bag. You will use the methods of 6.3 for the proportions and 6.1 for the mean. For the Bonus, you will use the sample size formula on page 338. You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found under Tools for Success in Course Home. Here is also a link: http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html. You can also find additional help on both confidence intervals and StatCrunch in the Online Math Workshop under Tab: “MAT300 Archived Workshops”. Specifically you will be looking for Confidence Intervals and Using Technology – CI. Submit your answers in Excel, Word or pdf format. Submit your file through the M&M® project link in the weekly course content. If calculating by hand, be sure to keep at least 4-6 decimal places for the sample proportions to eliminate large rounding errors. Answers 3 pts. Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies. 95% Confidence Interval for proportion is given by [pic] where p = x/n = 810/4049 = 0.200049395, [pic]= 1.959963985, n = 4049 Therefore, CI is given by, [pic] = (0.187727588, 0.212371202) Thus with 95% confidence we can claim that the proportion of blue M&Ms® candies is within (18.77%, 21.24%). Details |Confidence Interval Estimate for Proportion ......

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...a. The average (mean) annual income was less than $50,000 Null Hypothesis: The average annual income was greater than or equal to $50,000 H₀: µ > 50000 Alternate Hypothesis: The average annual income was less than $50,000. Ha: µ > 50000 Analysis Plan: Significance Level, α=0.05. Since the sample size, n > 30 I will use z-test for mean to test the given hypothesis. As the alternative hypothesis is Ha: µ > 50000, the given test is a one-tailed z-test. Critical Value and Decision Rule: The critical value for significance level, α=0.05 for a lower-tailed z-test is given as-1.645. Decision Rule: Reject H₀, if z – statistic, -1.645 Test Statistic - minitab One-Sample Z: Income ($1000) Test of mu = 50 vs < 50 The assumed standard deviation = 14.55 95% Upper Variable N Mean StDev SE Mean Bound Z P Income ($1000) 50 43.48 14.55 2.06 46.86 -3.17 0.001 Interpretation of Results and Conclusion: Since the P-value (0.0001) is smaller than the significance level (0.05), we reject the null hypothesis. The p-value implies the probability of rejecting a true null hypothesis. The significance level of 0.05, there is enough evidence to support the claim that the average annual income was less than $50,000. Confidence Interval - minitab One-Sample Z The assumed standard deviation = 14.55 ...

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