Descriptive Statistics and Interpretation

Anonymous
timer Asked: Aug 8th, 2014

Question Description


Our organization was Stabucks and the problem was recycling

Create a Microsoft®Excel® spreadsheet with the two variables from your learning team's dataset.

Analyze the data with MegaStat®, StatCrunch®, Microsoft® Excel®or other statistical tool(s), including:

(a) Descriptive stats for each numeric variable

(b) Histogram for each numeric variable

(c) Bar chart for each attribute (non numeric) variable

(d) Scatter plot if the data contains two numeric variables

Determine the appropriate descriptive statistics.

(a) For normally distributed data use the mean and standard deviation.

(b) For significantly skewed data use the median and interquartile range.

Usethe Individual Methodology Findings Templateto complete the descriptive statistics.

Use
 the Descriptive Statistics and Interpretation Exampleto develop an interpretation of the descriptive statistics.

Formatyour paper consistent with APA guidelines.

Submit both the spreadsheet and the completed Individual Methodology Findings Template.

Click the Assignment Files tab to submit your assignment.

Donna's sampling_design (3).docx 

qnt561_r7_individual_methodology_findings_template_week4.doc 

qnt561_r7_descriptive_statistics_and_interpretation_example_week4.doc 

Running Head: SAMPLING AND DATA COLLECTION PLAN Sampling and Data Collection Plan Donna Allare QNT/561 August 4, 2014 Heidi Carty 1 SAMPLING AND DATA COLLECTION PLAN 2 Sampling and Data Collection Plan Many critics believe DOTA will struggle to reach its desired goals for recycling cups in the coming years (Recycling & Reducing Waste, n.d. ). While many of these shortcomings are due to the inability to recycle hot cups, this study will focus on the presence of store front recycling units and its relationship with the number of cups recycled at DOTA stores (Recycling & Reducing Waste, n.d.). The independent variable that will be sampled in this study will be the presence of frontof-store recycling units at a given DOTA coffeehouse. The dependent variable which will be observed will be the numbers of cups recycled. First, the approximately 23,000 stores DOTA stores will be split into two categories, those that have store front recycling units and those that do not (Recycling & Reducing Waste, n.d.). Of these, 1000 of each will be chosen via simple random selection (to eliminate bias). The sample size, therefore, will be 1000 for each of the two categories. A smaller number could be chosen to make analysis easier, but a larger sample size will increase the accuracy and credibility of the study. The sample size used for this study is sufficient, given the analysis shown in the appendix, as it is well above the recommended sample size obtained from a 95% confidence interval and a 5% margin of error. Next, the number of cups recycled by each store per year will be determined by examination of the recycling records kept by each store. While choosing a particular month may make the analysis easier, using the entire year will avoid inconsistencies between stores that have peak sales during tourist months or marginal sales during months of poor weather. Utilizing, the SAMPLING AND DATA COLLECTION PLAN 3 entire year, should help standardize for location based customer dynamics, and will similarly increase the accuracy and credibility of the study. The data will physically be obtained by requesting for recycling records from stores. Stores should be able to provide accounting records of cups recycled, but in the rare instance a store is unable to deliver the required data, another store will be chosen at random using the aforementioned sampling method, to replace this store. After the data is collected and obtained, it will be stored on a secure computer and will be shared amongst the researchers. Great care will be taken to ensure DOTA’s privacy and the researchers will ensure the data is not made available inadvertently to parties who are not involved in the research. Utmost care will be taken to ensure the data is not lost or tampered with and proper research integrity is maintained. A fortunate aspect of this study will be the lack of risk involved to human subjects or to customers. There will be no adverse effect on DOTA’s consumers by the implementation of this research, so there should be little hesitation on DOTA’s part to cooperate with the researchers. Overall, this study will aim to determine if, in fact, there is a relationship between the presence of recycling units in front of DOTA stores and the number of cups recycled. The null hypothesis of this study will be that the sample mean of cups recycled in stores that do not have store-front recycling units, (𝜇1 ) , will be the same as the sample mean of cups recycled in stores that have store-front recycling units, (𝜇2 ). On the other hand, the alternate hypothesis will be that the sample mean of cups recycled in stores that do not have store-front recycling units, (𝜇1 ) , will be different than the sample mean of cups recycled in stores that have store-front recycling units, (𝜇2 ). 𝐻𝑦𝑝𝑡𝑜ℎ𝑒𝑠𝑒𝑠 𝑡𝑜 𝑏𝑒 𝑡𝑒𝑠𝑡𝑒𝑑: 𝐻𝑜: 𝜇1 = 𝜇2 , 𝐻𝑎: 𝜇1 ≠ 𝜇2 SAMPLING AND DATA COLLECTION PLAN As mentioned before, reliability of this study will be obtained by using a sample size larger than the recommended sample size given a 95% confidence interval and 5% margin of error. Additionally, the sample mean will represent cups recycled during the entire year to standardize for location specific customer dynamics. Validity of the study will be achieved by ensuring that a SRS is utilized to collect the data, and the integrity of the data does not become compromised. Special care will be taken to ensure the data is secured and all statistical work be done accurately. Special care will be taken to ensure that all statistical estimates are valid. For instance, the recommended sample mean, is shown to be a valid estimate and the confidence interval a valid indicator of the sample mean, given the fulfillment of the criteria discussed in Appendix 1. Overall, this experimental design will be made reliable and valid not only through the collection of proper data, but the high effective work of the researchers performing this study. 4 SAMPLING AND DATA COLLECTION PLAN 5 Appendix 1: Recommended Sample Size for 95% CI and 5% ME: Note: In order to calculate a sample size, we would need to have an idea about the standard deviation in cups recycled, which is data we do not have, prior to carrying out this study. However, an alternative approach we can use is to use the proportion of stores having in front of store recycling units to calculate our recommended sample size. 𝑀𝐸 = 𝑧√ (𝑝̂)(1−𝑝̂) 𝑛 𝑧 , solving for n yields: 𝑛 = (𝑀𝐸)2 (𝑝̂ )(1 − 𝑝̂ ) (See References 1, 3 and 4 for more info). Now, we are given ME =.05, the z-score corresponding to a 95 Confidence Interval is 1.96, and the proportion of stores having store front recycling units will need to be determined. The proportion of stores having recycling units in front of their stores was 5% in 2011, since then DOTA has claimed at most a 67% per year increase in 2013. It can be assumed the percentage was less than that on average per year over the last 3 years (Recycling & Reducing Waste, n.d.). In order to achieve the most accurate sample size, we should assume that the increase per year was 67%. This will maximize the denominator in the equation shown below, thus producing a sample size that overcompensates for or lack of an accurate statistic, and will still therefore be reliable (See references 1, 3, and 4 for more info). 𝑝̂ = (5%)(1.67)(2014-2011)=(23.29%), therefore the sample size will be: 𝑧 2 1.96 2 ) (𝑝̂ )(1 − 𝑝̂ ) = ( ) (. 23)(1 − .23) = 272.1 𝑀𝐸 . 05 𝑛=( SAMPLING AND DATA COLLECTION PLAN (See References 1, 3, and 4 for more info). This estimate can be considered reasonably accurate because: (i) The sample is a SRS and was obtained from a binomial population (either have store front recycling or do not have store front recycling). (ii) Both n𝑝̂ ≥10 and n𝑝̂ (1 − 𝑝̂ ) ≥10 (See references 1, 3, and 4). (iii) The size of the population (23,000+) is at least 10 times the size of the sample. Therefore, we can assume that if our sample size is greater than 272.14, our study will produce reliable results (See References 1, 3, and 4 for more info). 6 SAMPLING AND DATA COLLECTION PLAN 7 References 1 Hypothesis Testing of the Difference Between Two Populations Means. (n.d.). Retrieved July 31, 2014, from http://www.kean.edu/~fosborne/bstat/07b2means.html 2 Recycling & Reducing Waste| Starbucks Coffee Company | Starbucks Coffee Company. (n.d.). Retrieved July 31, 2014, from http://www.starbucks.com/responsibility/environment/recycling 3 Statistics Notes Class 23: Retrieved July 31, 2014, from http://www.unc.edu/~rls/s1512010/class23.pdf 4 Statistics Slides Class 10: Retrieved July 31, 2014, from http://www.csun.edu/~an73773/SlidesClass10F09.pdf
Running head: DESCRIPTIVE STATISTICS 1 Descriptive Statistics Name QNT/561 Date Instructor’s Name DESCRIPTIVE STATISTICS 2 Descriptive Statistics Determine the appropriate descriptive statistics. Note: If the data was normally distributed, use the mean and standard deviation. If the data was skewed significantly, use the median and interquartile range. Numeric Variable Name1 Distribution: State if not normally distributed Central Tendency: Dispersion: Number: Min/Max: Confidence Interval: (if distribution is normal) Numeric Variable Name2 (if applicable) Distribution: State if not normally distributed Central Tendency: Dispersion: Number: Min/Max: Confidence Interval: (if distribution is normal) Attribute Variable Name (if applicable) Create a bar chart. Describe the proportions. DESCRIPTIVE STATISTICS Descriptive Statistics Interpretation Numeric Variable Name1 Describe the variable in laymen terms. Numeric Variable Name2 (if applicable) Describe the variable in laymen terms. 3 DESCRIPTIVE STATISTICS 4 Appendix A Raw data used in the analysis Fit data to one page. DESCRIPTIVE STATISTICS 5 Appendix B Charts and Tables This part of the paper will include items that are then cited in the body of the paper. Usually, large items are placed here not to distract from reading the paper. DESCRIPTIVE STATISTICS 6 Appendix C Descriptive Statistics This part of the paper will include descriptive statistics.
Running Head: SAMPLING AND DATA COLLECTION PLAN Sampling and Data Collection Plan Donna Allare QNT/561 August 4, 2014 Heidi Carty 1 SAMPLING AND DATA COLLECTION PLAN 2 Sampling and Data Collection Plan Many critics believe DOTA will struggle to reach its desired goals for recycling cups in the coming years (Recycling & Reducing Waste, n.d. ). While many of these shortcomings are due to the inability to recycle hot cups, this study will focus on the presence of store front recycling units and its relationship with the number of cups recycled at DOTA stores (Recycling & Reducing Waste, n.d.). The independent variable that will be sampled in this study will be the presence of frontof-store recycling units at a given DOTA coffeehouse. The dependent variable which will be observed will be the numbers of cups recycled. First, the approximately 23,000 stores DOTA stores will be split into two categories, those that have store front recycling units and those that do not (Recycling & Reducing Waste, n.d.). Of these, 1000 of each will be chosen via simple random selection (to eliminate bias). The sample size, therefore, will be 1000 for each of the two categories. A smaller number could be chosen to make analysis easier, but a larger sample size will increase the accuracy and credibility of the study. The sample size used for this study is sufficient, given the analysis shown in the appendix, as it is well above the recommended sample size obtained from a 95% confidence interval and a 5% margin of error. Next, the number of cups recycled by each store per year will be determined by examination of the recycling records kept by each store. While choosing a particular month may make the analysis easier, using the entire year will avoid inconsistencies between stores that have peak sales during tourist months or marginal sales during months of poor weather. Utilizing, the SAMPLING AND DATA COLLECTION PLAN 3 entire year, should help standardize for location based customer dynamics, and will similarly increase the accuracy and credibility of the study. The data will physically be obtained by requesting for recycling records from stores. Stores should be able to provide accounting records of cups recycled, but in the rare instance a store is unable to deliver the required data, another store will be chosen at random using the aforementioned sampling method, to replace this store. After the data is collected and obtained, it will be stored on a secure computer and will be shared amongst the researchers. Great care will be taken to ensure DOTA’s privacy and the researchers will ensure the data is not made available inadvertently to parties who are not involved in the research. Utmost care will be taken to ensure the data is not lost or tampered with and proper research integrity is maintained. A fortunate aspect of this study will be the lack of risk involved to human subjects or to customers. There will be no adverse effect on DOTA’s consumers by the implementation of this research, so there should be little hesitation on DOTA’s part to cooperate with the researchers. Overall, this study will aim to determine if, in fact, there is a relationship between the presence of recycling units in front of DOTA stores and the number of cups recycled. The null hypothesis of this study will be that the sample mean of cups recycled in stores that do not have store-front recycling units, (𝜇1 ) , will be the same as the sample mean of cups recycled in stores that have store-front recycling units, (𝜇2 ). On the other hand, the alternate hypothesis will be that the sample mean of cups recycled in stores that do not have store-front recycling units, (𝜇1 ) , will be different than the sample mean of cups recycled in stores that have store-front recycling units, (𝜇2 ). 𝐻𝑦𝑝𝑡𝑜ℎ𝑒𝑠𝑒𝑠 𝑡𝑜 𝑏𝑒 𝑡𝑒𝑠𝑡𝑒𝑑: 𝐻𝑜: 𝜇1 = 𝜇2 , 𝐻𝑎: 𝜇1 ≠ 𝜇2 SAMPLING AND DATA COLLECTION PLAN As mentioned before, reliability of this study will be obtained by using a sample size larger than the recommended sample size given a 95% confidence interval and 5% margin of error. Additionally, the sample mean will represent cups recycled during the entire year to standardize for location specific customer dynamics. Validity of the study will be achieved by ensuring that a SRS is utilized to collect the data, and the integrity of the data does not become compromised. Special care will be taken to ensure the data is secured and all statistical work be done accurately. Special care will be taken to ensure that all statistical estimates are valid. For instance, the recommended sample mean, is shown to be a valid estimate and the confidence interval a valid indicator of the sample mean, given the fulfillment of the criteria discussed in Appendix 1. Overall, this experimental design will be made reliable and valid not only through the collection of proper data, but the high effective work of the researchers performing this study. 4 SAMPLING AND DATA COLLECTION PLAN 5 Appendix 1: Recommended Sample Size for 95% CI and 5% ME: Note: In order to calculate a sample size, we would need to have an idea about the standard deviation in cups recycled, which is data we do not have, prior to carrying out this study. However, an alternative approach we can use is to use the proportion of stores having in front of store recycling units to calculate our recommended sample size. 𝑀𝐸 = 𝑧√ (𝑝̂)(1−𝑝̂) 𝑛 𝑧 , solving for n yields: 𝑛 = (𝑀𝐸)2 (𝑝̂ )(1 − 𝑝̂ ) (See References 1, 3 and 4 for more info). Now, we are given ME =.05, the z-score corresponding to a 95 Confidence Interval is 1.96, and the proportion of stores having store front recycling units will need to be determined. The proportion of stores having recycling units in front of their stores was 5% in 2011, since then DOTA has claimed at most a 67% per year increase in 2013. It can be assumed the percentage was less than that on average per year over the last 3 years (Recycling & Reducing Waste, n.d.). In order to achieve the most accurate sample size, we should assume that the increase per year was 67%. This will maximize the denominator in the equation shown below, thus producing a sample size that overcompensates for or lack of an accurate statistic, and will still therefore be reliable (See references 1, 3, and 4 for more info). 𝑝̂ = (5%)(1.67)(2014-2011)=(23.29%), therefore the sample size will be: 𝑧 2 1.96 2 ) (𝑝̂ )(1 − 𝑝̂ ) = ( ) (. 23)(1 − .23) = 272.1 𝑀𝐸 . 05 𝑛=( SAMPLING AND DATA COLLECTION PLAN (See References 1, 3, and 4 for more info). This estimate can be considered reasonably accurate because: (i) The sample is a SRS and was obtained from a binomial population (either have store front recycling or do not have store front recycling). (ii) Both n𝑝̂ ≥10 and n𝑝̂ (1 − 𝑝̂ ) ≥10 (See references 1, 3, and 4). (iii) The size of the population (23,000+) is at least 10 times the size of the sample. Therefore, we can assume that if our sample size is greater than 272.14, our study will produce reliable results (See References 1, 3, and 4 for more info). 6 SAMPLING AND DATA COLLECTION PLAN 7 References 1 Hypothesis Testing of the Difference Between Two Populations Means. (n.d.). Retrieved July 31, 2014, from http://www.kean.edu/~fosborne/bstat/07b2means.html 2 Recycling & Reducing Waste| Starbucks Coffee Company | Starbucks Coffee Company. (n.d.). Retrieved July 31, 2014, from http://www.starbucks.com/responsibility/environment/recycling 3 Statistics Notes Class 23: Retrieved July 31, 2014, from http://www.unc.edu/~rls/s1512010/class23.pdf 4 Statistics Slides Class 10: Retrieved July 31, 2014, from http://www.csun.edu/~an73773/SlidesClass10F09.pdf
Running head: DESCRIPTIVE STATISTICS 1 Descriptive Statistics Name QNT/561 Date Instructor’s Name DESCRIPTIVE STATISTICS 2 Descriptive Statistics Determine the appropriate descriptive statistics. Note: If the data was normally distributed, use the mean and standard deviation. If the data was skewed significantly, use the median and interquartile range. Numeric Variable Name1 Distribution: State if not normally distributed Central Tendency: Dispersion: Number: Min/Max: Confidence Interval: (if distribution is normal) Numeric Variable Name2 (if applicable) Distribution: State if not normally distributed Central Tendency: Dispersion: Number: Min/Max: Confidence Interval: (if distribution is normal) Attribute Variable Name (if applicable) Create a bar chart. Describe the proportions. DESCRIPTIVE STATISTICS Descriptive Statistics Interpretation Numeric Variable Name1 Describe the variable in laymen terms. Numeric Variable Name2 (if applicable) Describe the variable in laymen terms. 3 DESCRIPTIVE STATISTICS 4 Appendix A Raw data used in the analysis Fit data to one page. DESCRIPTIVE STATISTICS 5 Appendix B Charts and Tables This part of the paper will include items that are then cited in the body of the paper. Usually, large items are placed here not to distract from reading the paper. DESCRIPTIVE STATISTICS 6 Appendix C Descriptive Statistics This part of the paper will include descriptive statistics.
Descriptive Statistics and Interpretation Example QNT/561 Version 7 1 University of Phoenix Material Descriptive Statistics and Interpretation Example Interpretation Phrases Central Tendency: Mean = average of a set of data Median = half or equal number of data is above and half or equal number of data is below. It is a midpoint in an ordered (sorted) set of data, a physical location Mode = most frequent value in a set of data Dispersion: Standard deviation = variation Interquartile range (IQR) = the middle 50% of the data Range = the difference between the largest and smallest value of the data Confidence Interval: (data must be normal) There is 95% confidence that the population average is between _____ and ____ units. Normal or significantly skewed data: MegaStat: Descriptive statistics Normal curve goodness of fit p-value • • Normal, p-value > .05 Significantly Skewed, p-value < .05 Histogram: Eyeball the histogram. • • Normal data will have a symmetrical or slightly skewed shape. Significantly Skewed shape will have extreme skewness Use phrase combinations: Normally distributed: Mean and Standard Deviation, Not normally distributed: Median and IQR Copyright © 2014 by University of Phoenix. All rights reserved. Descriptive Statistics and Interpretation Example QNT/561 Version 7 2 Descriptive Statistics Body Weight (Lbs.) Central Tendency: Mean = 149 Lbs. Dispersion: Standard deviation = 30 Lbs. Count: 100 Min/Max: 99 pounds and 234 Lbs. Confidence Interval: 144 to 155 Lbs. See the histogram in Appendix A, and descriptive statistics in Appendix B. Age Distribution is not normally distributed Central Tendency: Median = 36 years Dispersion: Interquartile Range = 20.5 years / 2 = ± 10 years Count: 100 Min/Max: 18 years and 74 years Confidence Interval: Not applicable (data is not normally distributed) See the histogram in Appendix A, and descriptive statistics in Appendix B. A scatter plot is in Appendix C. Education Level Thirteen percent of the subjects have no high school degree while 44% have high school degree. Forty three percent have a college or college graduate degree. See the bar chart in Appendix D. Copyright © 2014 by University of Phoenix. All rights reserved. Descriptive Statistics and Interpretation Example QNT/561 Version 7 3 Descriptive Statistics Interpretation Interpretation Body Weight One hundred subjects were randomly selected. Their body weight was observed between 99 and 234 pounds. Their average weight was 149 pounds, with a variation of plus or minus 30 pounds. One half or more were above 149 pounds. There is 95% confidence that the population body weight average is between 144 and 155 pounds. Age The data was significantly skewed. One hundred subjects were randomly selected. Their ages were between 18 and 74 years, with a variation of plus or minus 10 years. One half or more subjects were 36 years of age or older. The middle half of the subjects’ ages fell between 27 and 47 years. The most frequent age was 36 years. Copyright © 2014 by University of Phoenix. All rights reserved. Descriptive Statistics and Interpretation Example QNT/561 Version 7 APPENDIX A Body Weight and Age Histograms Copyright © 2014 by University of Phoenix. All rights reserved. 4 Descriptive Statistics and Interpretation Example QNT/561 Version 7 APPENDIX B Descriptive Statistics Body Weight and Age Copyright © 2014 by University of Phoenix. All rights reserved. 5 Descriptive Statistics and Interpretation Example QNT/561 Version 7 APPENDIX C Scatterplot Body Age versus Weight Copyright © 2014 by University of Phoenix. All rights reserved. 6 Descriptive Statistics and Interpretation Example QNT/561 Version 7 APPENDIX D Bar Chart Education Level Copyright © 2014 by University of Phoenix. All rights reserved. 7

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