Western Region Original Price Sale Price Days to Sell 82 60 20 140 123 26 80 70 16 89 50 72 135 120 18 146 143 109 80 80 79 125 100 130 70 60 100 81 52 96 103 95 14 118 100 33 136 100 101 101 50 55 140 75 69 73 42 120 135 99 90 89 40 40 144 60 130 109 65 23 145 100 61 81 50 133 136 70 62 80 80 4 137 137 101 102 50 30 75 42 98 71 62 189 109 89 122 130 119 108 108 89 19 146 100 125 98 80 15 82 50 7 79 79 1 138 99 17 95 79 23 136 129 30 74 34 17 139 100 25 143 89 120 120 109 35 75 75 25 136 69 15 124 100 75 Eastern Region Original Price Sale Price 148 139 103 89 112 100 81 61 136 100 112 89 121 100 83 60 99 80 93 65 98 70 106 100 109 99 102 89 96 96 103 40 84 60 96 50 125 85 136 100 103 103 95 95 149 100 92 88 111 100 108 70 98 68 102 82 109 100 137 137 85 65 94 84 141 141 131 120 130 120 107 80 113 80 142 100 105 60 140 70 83 43 97 90 95 90 129 99 93 60 132 91 80 54 68 Mean Median Range Std Dev Minimum Maximum 25 33 49 100 75 Western Region Sale Price Original Price Higher Lower Outlier Higher Lower 69 79 50 54 58 107.2 105.5 92 27.85 54 146 79.48 79 109 26.95 34 143 163 51 133 26 118 89 73 79 103 Eastern Region Days to Sell Original Price Sale Price 61.6 107.88 85.74 52 103 88.5 188 76 101 45.43 19.52 23.00 1 73 40 189 149 141 152 -29 3 No No 100 80 60 60 70 147 69 132 40 4 137, 143 No No 189 No No 137, 139,141 90% confidence Interval 6.27 10.57 79.48+/-6.2761.60+/-10.57 Margin of error in % Sample Size 0.06 40 120 $ % of two means 5.35 85.74+/-5.35 74.14% 89 0.05 43 125 $ 79.48% 99 rn Region Days to Sell 33 59 189 145 91 66 81 65 100 15 34 102 45 166 50 56 53 71 45 80 33 1 23 45 77 20 65 34 144 2 34 45 100 8 10 45 120 100 36 75 69 45 38 56 71 34 55 67 78 114 Days to Sell 63.8 56 188 40.77 1 189 145 -18 145, 166, 189 No 9.48 63.8+/-9.48 Running head: GUIDE TO WRITING WITH STATISTICS MTH410 Guide to Writing with Statistics CSU-Global Campus October, 2014 1 GUIDE TO WRITING WITH STATISTICS 2 Introduction The purpose of this paper is to provide some general guidance in the writing of papers using statistics and associated tests. The paper provides some general tips for writing and the use of statistics. An example prompt is included, followed by a sample paper. General Tips for Writing a Math Paper: Organization: o Turn your prompt into headings for paper sections. This will help you to make sure you include all of the required information and analysis. It also helps the reader identify the material. o Your paper needs: A separate title page using APA style requirements (running header, page numbers, course, instructor, your name, date, etc.). An introduction (often a summary or abstract of the problem). A body of the paper that answers the questions posed in the problem and includes calculations and graphs associated with this problem. This is where you can turn your prompt into headings. All references need to be properly cited. A conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. A separate sheet for references. o There are templates that use APA style that you can insert your material into. If you really struggle with formatting, this may be an option for your first paper or two. If you use a template, remember to double-check it to remove any extra instructions or pages or other elements that weren't used. In general, numbers less than 10 are to be written in word form. However, if you have numbers in this range that carry decimals, write them in numeral form. Never use or interpret a statistic or test that you don't fully understand. Target your audience and present as much information as necessary to allow the reader to make an independent interpretation. Make use of graphs and tables to display information in an easily understood manner. Format them the same throughout, and make sure you don't manipulate axes. If you are referring to a statistic that is less commonly used, explain how you calculated it. (It is not necessary to explain mean, but it may be necessary to explain how you set up an ANOVA test.) Be clear about your sample and its corresponding population. Be direct in writing descriptive statistics (The mean in Group A is 22.9 units.). Translate the meaning of the statistic for the reader. Write plainly and then back it up with statistical evidence. For example: Men and women scored equally well on this study (t = 0.25, p < 0.01). GUIDE TO WRITING WITH STATISTICS For additional resources see the CSU-Global Guide to Writing and APA Requirements or visit https://owl.english.purdue.edu/owl/owlprint/672/ 2 GUIDE TO WRITING WITH STATISTICS 3 Prompt for Sample Paper: Critical Thinking: Heavenly Chocolates Website transactions are an important segment of sales and distribution today. Heavenly Chocolates manufactures and sells quality chocolates at its plant and retail store in Bozeman, MT. Three years ago, the company developed a website and began sales on the internet. Website sales have exceeded expectations and management is now considering strategies to continue to increase its sales. To learn more about its sales, Heavenly Chocolates selected a sample of 50 random transactions from its previous month's sales. The transaction data shows the day of the week the purchase was made, the type of browser used in the transaction, the time spent on the website, the number of website pages viewed, and the amount spent by the customer. The data is shown in a file named Chocolate. Heavenly Chocolates would like to determine if time spent on the website or the number of pages viewed influence the total purchase. They would also like to examine any effect that day of the week and browser type have on sales. Managerial Report Prepare a report (see below) using the numerical methods of descriptive statistics presented in this module to learn how the variables contribute to the sales of chocolate. Be sure to include the following four (4) items in your report. 1. Descriptive statistics (mean, median, range, and standard deviation) for each of the three variables along with an explanation of what the descriptive statistics tell us about the sales. 2. A breakdown using descriptive statistics examining the effect of days of the week on sales. Evaluate the results. 3. A breakdown using descriptive statistics examining the effect of browser type on sales. Evaluate the results. 4. Descriptive statistics (correlation coefficient) showing the relationship between sales (in dollars), and each of the other two variables. Evaluate the relationships between sales (in dollars) and each of the other variables (time spent and pages visited). Use tables, charts, graphs, or visual dashboards to support your conclusions. Make recommendations for continuing to develop sales to the management. Write a report that adheres to the Written Assignment Requirements under the heading \"Expectations for CSU-Global Written Assignments\" found in the CSU-Global Guide to Writing and APA Requirements. As with all written assignments at CSU-Global, you should have in-text citations and a reference page. Your report must contain the following: A title page An introduction GUIDE TO WRITING WITH STATISTICS 4 A body of the paper that answers the questions posed in the problem and calculations and graphs associated with this problem. A conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. Submit your Excel file in addition to your report. Note: Prompt adapted from the \"Heavenly Chocolate Website Transactions Case Problem 4,\" D. Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for business and economics. (7th ed.), p. 167,168. The following pages contain the sample paper corresponding to the prompt written above. Read through it for ideas on how to write your own papers. HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) Heavenly Chocolates Web Sales Analysis Student Name MTH410 - Quantitative Business Analysis Colorado State University-Global Campus Instructor Name Date 1 HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 2 Heavenly Chocolates Web Sales Analysis Website transactions are an important segment of sales and distribution today. Any business developing a market for online sales would be wise to analyze data from both the general marketplace and its own specific customer segment. Analysis of this data can provide insight into further development of sales. Heavenly Chocolates data-mined their transactions for the previous month to gather a random sample of 50 customer transactions. The sample recorded the day of the week the purchase was made, the type of browser used in the transaction, the time spent on their website, the number of website pages viewed, and the amount spent by the customer. The purpose of this analysis is to determine if the time spent on the website or the number of pages viewed influences the total purchase. The impact of day of the week and browser type on sales will also be studied. Overview of Online Sales The 50 customers sampled spent a total of $3,406.41 in the previous month. This is an average of $68.10 per customer. The purchases ranged from a $17.80 to $158.50. The average customer spent 12.8 minutes on the website. Time spent on the website ranged from 4.3 minutes to 32.9 minutes. The typical customer viewed almost five pages, with two as the minimum and ten as the maximum. The data set is summarized below in Table 1. Table 1 Summary of Online Sales Sample Time (min) Pages Viewed Amount Spent ($) mean 12.8 4.8 68.1 median 11.4 4.5 62.2 std dev 6.1 2 32.3 min 4.3 2 17.8 HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 3 Table 1 Summary of Online Sales Sample (Continued) Time (min) Pages Viewed Amount Spent ($) max 32.9 10 158.5 range 28.6 8 140.7 SUM ($) 3406.41 Note: Data compiled from the \"Heavenly Chocolate Website Transactions Case Problem 4,\" D. Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for business and economics. (7th ed.), p. 167,168. Impact of Day of the Week on Sales The daily sales breakdown reveals some interesting patterns. Sunday is the lowest sales day, from the perspective of both total sales ($218.15) and average sales ($43.60). Monday and Friday were the best days in terms of overall sales performance. Monday had the highest mean (average) sales at $90.40, while Friday had the highest total sales at $945.43 for roughly 28% of the sample total. See Table 2 for a complete breakdown of the impact of the day of the week on amount spent, time spent on the website, and number of pages viewed. Table 2 Breakdown of Sales by Day of the Week Sun Mon Tues Wed Thurs Fri Sat Total mean 43.6 90.4 59.3 57 58.8 85.9 54.1 68.1 median 37.2 104.2 67.4 53.4 59.2 70.4 55.6 62.2 std dev 12.8 43.5 14.6 24.5 30.4 33.9 17.7 32.3 min 32.7 26.7 39.1 32.7 17.8 52.1 27.9 17.8 max 64.2 158.5 74.4 94.9 91.6 155.3 78.6 158.5 range 31.4 131.8 35.4 62.2 73.8 103.2 50.7 140.7 count 5 9 7 6 5 11 7 50 Total Sales HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 4 Table 2 Breakdown of Sales by Day of the Week (Continued) Sun SUM ($) 218.15 Mon Tues Wed Thurs Fri Sat Total 813.38 414.86 341.82 294.03 945.43 378.74 3,406.41 Time Spent mean median 11.4 11.7 15.3 13.3 12.7 10.6 12.4 12 10.9 8.1 12.3 9.7 13.2 13.3 12.8 11.4 std dev 2.2 7.4 6 4.8 7.1 7.8 4.3 6.1 min 8 7.3 7.8 5 6.2 4.3 6 4.3 max 14.3 30.1 24.7 19.5 23.3 32.9 18.1 32.9 range 6.3 22.8 16.9 14.5 17.1 28.6 12.1 28.6 Pages Viewed mean 4.2 6.4 4 4.2 3.8 4.8 5.3 4.8 median 4 6 4 4.5 4 4 5 4.5 std dev 1.9 2.1 2.1 1.5 2 2.3 1.1 2 min 2 4 2 2 2 3 4 2 max 7 10 7 6 7 10 7 10 range 5 6 5 4 5 7 3 8 Note: Data compiled from the \"Heavenly Chocolate Website Transactions Case Problem 4,\" D. Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for business and economics. (7th ed.), p. 167,168. By almost every measure, Monday is the best day for sales. Friday follows closely (see Table 2). It makes logical sense to recommend that the marketing department develop advertising targeted for Monday and Friday. Weekends are subpar and midweek statistics are nearly equivalent. Targeting sales or special packages for midweek may produce some increased traffic. If these recommendations are implemented, follow-up analysis is recommended to see if the desired results are being produced. Impact of Browser on Sales HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 5 There were also sales differences revealed by breaking the data down by browser type. Customers using Internet Explorer to complete their transactions accounted for the highest total sales at $1,656.81; however, this value was achieved on volume (see Table 3). Internet Explorer had the lowest average sale at $61.36 while Firefox customers averaged $76.80 per transaction. Table 3 Breakdown of Sales by Browser Firefox Internet Explorer Other Total mean 76.8 61.36 74.5 68.1 median 68 55.6 67.4 62.2 std dev 38.9 29.2 24.6 32.3 min 27.9 17.8 52.2 17.8 max 158.5 126.4 120.3 158.5 range 130.6 108.6 68.1 140.7 count 16 27 7 50 SUM ($) 1,228.21 1,656.81 521.39 3,406.41 Note: Data compiled from the \"Heavenly Chocolate Website Transactions Case Problem 4,\" D. Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for business and economics. (7th ed.), p. 167,168. The opportunity here is to target premium packages for advertising specific to Firefox. Value packages could be created for advertising specific to Internet Explorer. This promotion should be combined with the recommendations given regarding days of the week and subjected to a follow-up analysis to check for results. Relationship between Amount Spent and Website Use The other feature of this analysis is to evaluate the relationship between amount spent by customers and how much time they spent on the website with the additional variable of number HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 6 of pages viewed also taken into account. For this, a correlation analysis was performed. The correlation coefficient between time spent on the website and amount spent in dollars was moderately positive (r = 0.58). A similar moderately positive correlation coefficient (r = 0.60) was found between the variables of time spent on the website and number of pages visited. The strongest correlation was found between number of pages viewed on the website and amount spent. This correlation coefficient (r = 0.72) approaches a strong positive correlation (see Figure 1). This suggests that there may be some merit in trying to guide customers to view more pages. 180.00 160.00 140.00 120.00 100.00 Dollars Spent 80.00 60.00 40.00 20.00 0.00 1 2 3 4 5 6 7 8 9 10 11 Pages Viewed Figure 1. Relationship Between Pages Viewed and Dollars Spent. Data compiled from the \"Heavenly Chocolate Website Transactions Case Problem 4,\" D. Anderson, D. Sweeney, T. Williams, J. Camm, & J. Cochran, 2015, Essentials of statistics for business and economics. (7th ed.), p. 167,168. A common tactic is to guide customers to pages that have also been viewed by other customers viewing the product on the current page. Another suggestion is to pair pages and suggest that customers who purchased the product on the current page also frequently purchased a product on the linked page. As with previous suggestions, follow-up analysis should be performed to check results. On a cautionary note, this can be overdone. The statement from HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) 7 Essentials of Statistics for Business and Economics that correlation is a measure of linear association and not causation should also be duly noted (Anderson, et al., 2015). Conclusion The analysis of this sample of 50 random customer transactions revealed several items to be used in the development of continued growth at Heavenly Chocolate. There is positive correlation between all three variables, but the strongest correlation is between number of pages viewed and amount of sales. There is adequate reason to pursue linking pages and making suggestions for customer purchasing. Monday and Friday are the best sales days. Firefox customers spend the most, but Internet Explorer customers provide the highest volume. Packaging and marketing strategies can be developed using this information. This analysis validates the use of statistical tools to provide insight into new strategies. Follow-up analysis is also mandated to find out if the strategies are producing results. HEAVENLY CHOCOLATES WEB SALES ANALYSIS (Sample) References Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochran, J.J. (2015). Essentials of statistics for business and economics. (7th ed.). Stamford, CT: Cengage Learning. 8 Instructions: Report and citations in APA formatting introduction needs to summarize the problem. body of the paper needs to answer the questions posed in the problem by communicating the results of your analysis. Include results of calculations, as well as charts and graphs, where appropriate. conclusion paragraph addresses findings and what is determined from the data and analysis. Completed Excel file in addition to report. (attached in question) No content from other students papers. Beltway Shoe Company sells luxury leather shoes in the United States. The company monitors its shoe sales by collecting randomly chosen data from store locations throughout the country. They record original price, sale price, and number of days it takes to sell each unit. Each pair of shoes is classified as \"Eastern Region" if it is sold in the Eastern part of the United States, or as \"Western Region" if it is sold in the Western part of the country. Randomly chosen samples provided sales data for 50 Western Region and 50 Eastern Region pairs of shoes. The complete data set is in the file named Shoes, linked at the bottom of the page. Managerial Report Prepare a report (see below) that summarizes your assessment of the nature of the shoe market in each region. Be sure to include the following seven (7) items in your report. 1. Descriptive statistics (mean, median, range, and standard deviation) to summarize each of the three variables for the 50 Western Region shoes. Are there any outliers in the data set for any of the three variables? If there are any outliers in any category, please list them and state for which category they are an outlier. Describe which method you used to make your determination. 2. Descriptive statistics (mean, median, range, and standard deviation) to summarize each of the three variables for the 50 Eastern Region shoes. Are there any outliers in the data set for any of the three variables? If there are any outliers in any category, please list them and state for which category they are an outlier. Describe which method you used to make your determination. 3. Compare your summary results from #1 and #2. Discuss any specific statistical results that would help the Beltway Shoes Marketing Department understand the regional shoe market. 4. Develop a 90% confidence interval estimate of the population mean sales price and population mean number of days to sell for pairs of Beltway Shoes in the Eastern Region. Interpret your results. 5. Develop a 90% confidence interval estimate of the population mean sales price and population mean number of days to sell for pairs of Beltway Shoes in the Western Region. Interpret your results. 6. Assume a branch sales manager requested estimates of the mean selling price of Western Region shoes with a margin of error of $5 and the mean selling price of Eastern Region shoes with a margin of error of $4. Using 90% confidence, how large should the sample sizes be for each? 7. A Western Region store manager just placed on display a pair of Beltway Shoes, with an original price of $120. Also, an Eastern Region store manager just placed on display a pair of Beltway Shoes, with an original price of $125. For each pair of shoes, what is your estimate of the final selling price (based on the percent difference for the sale and list price) and number of days required to sell each of these units? Confidence interval for population mean for number of days to sell for eastern region Data Sample Standard Deviation 40.77 Sample Mean 63.8 Sample Size 50 Confidence Level 90% Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Value Interval Half Width 5.7657486938 49 1.6766 9.6666 Confidence Interval Interval Lower Limit Interval Upper Limit 54.13 73.47 Confidence Interval for population mean for sale price for eastern region Data Sample Standard Deviation 23 Sample Mean 85.74 Sample Size 50 Confidence Level 90% Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Value Interval Half Width 3.2526911935 49 1.6766 5.4533 Confidence Interval Interval Lower Limit Interval Upper Limit 80.29 91.19 Confidence interval for population mean for number of days to sell for western region Data Sample Standard Deviation 45.43 Sample Mean 61.6 Sample Size 50 Confidence Level 90% Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Value Interval Half Width 6.4247722139 49 1.6766 10.7715 Confidence Interval Interval Lower Limit Interval Upper Limit 50.83 72.37 Confidence Interval for Population mean for sales price for western region Data Sample Standard Deviation 26.95 Sample Mean 79.48 Sample Size 50 Confidence Level 90% Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Value Interval Half Width 3.8113055506 49 1.6766 6.3898 Confidence Interval Interval Lower Limit Interval Upper Limit 73.09 85.87 Western Region Eastern Region Western Region OWestern ReWestern RegioEastern Region O Eastern Regi 82 60 20 148 139 140 123 26 103 89 80 70 16 112 100 89 50 72 81 61 135 120 18 136 100 146 143 109 112 89 80 80 79 121 100 125 100 130 83 60 70 60 100 99 80 81 52 96 93 65 103 95 14 98 70 118 100 33 106 100 136 100 101 109 99 101 50 55 102 89 140 75 69 96 96 73 42 120 103 40 135 99 90 84 60 89 40 40 96 50 144 60 130 125 85 109 65 23 136 100 145 100 61 103 103 81 50 133 95 95 136 70 62 149 100 80 80 4 92 88 137 137 101 111 100 102 50 30 108 70 75 42 98 98 68 71 62 189 102 82 109 89 122 109 100 130 119 108 137 137 108 89 19 85 65 146 100 125 94 84 98 80 15 141 141 82 50 7 131 120 79 79 1 130 120 138 99 17 107 80 95 79 23 113 80 136 129 30 142 100 74 34 17 105 60 139 100 25 140 70 143 89 120 83 43 120 109 35 97 90 75 75 25 95 90 136 69 15 129 99 124 132 91 80 54 68 100 69 79 50 54 58 75 25 33 49 100 75 Western Region Sale Price Original Price Mean Median Range Std Dev Minimum Maximum Higher Lower Outlier Higher Lower 107.2 105.5 92 27.85 54 146 79.48 79 109 26.95 34 143 163 51 133 26 93 118 89 73 79 103 Eastern Region Days to Sell Original Price Sale Price 61.6 107.88 85.74 52 103 88.5 188 76 101 45.43 19.52 23.00 1 73 40 189 149 141 152 -29 3 No No 60 100 80 60 60 70 147 69 132 40 4 137, 143 No No 189 No No 137, 139,141 90% confidence Interval 6.27 10.57 79.48+/-6.2761.60+/-10.57 Margin of error in % Sample Size 0.06 40 120 $ % of two means 5.35 85.74+/-5.35 74.14% 89 0.05 43 125 $ 79.48% 99 rn Region Eastern Region Days to Sell 33 59 189 145 91 66 81 65 100 15 34 102 45 166 50 56 53 71 45 80 33 1 23 45 77 20 65 34 144 2 34 45 100 8 10 45 120 100 36 75 69 45 38 56 Western Region Original Price Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Eastern Region Original Price Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 71 34 55 67 78 114 Days to Sell 63.8 56 188 40.77 1 189 145 -18 145, 166, 189 No 9.48 63.8+/-9.48 gion Original Price 107.2 3.9386105496 105.5 80 27.8501822806 775.6326530612 -1.5241005528 -0.0383807245 92 54 146 5360 50 gion Original Price 107.88 2.7601597114 103 103 19.5172764912 380.9240816327 -0.5821283261 0.5115341955 76 73 149 5394 50 Western Region Sale Price Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 79.48 3.8118226397 79 100 26.9536563723 726.4995918367 -0.512088682 0.4229013866 109 34 143 3974 50 Eastern Region Sale Price Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 85.74 3.2521026166 88.5 100 22.9958381328 528.8085714286 0.1635549952 0.3481682227 101 40 141 4287 50 Western Region Days to Sell Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Eastern Region Days to Sell Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count n Days to Sell 61.6 6.424697 52 25 45.42947 2063.837 -0.51554 0.605697 188 1 189 3080 50 n Days to Sell 63.8 5.765343 56 45 40.76713 1661.959 1.243446 1.032431 188 1 189 3190 50 Confidence interval for population mean for number of days to sell for eastern region Data Sample Standard Deviation 40.77 Sample Mean 63.8 Sample Size 50 Confidence Level 90% Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Value Interval Half Width 5.7657486938 49 1.6766 9.6666 Confidence Interval Interval Lower Limit Interval Upper Limit 54.13 73.47 Confidence Interval for population mean for sale price for eastern region Data Sample Standard Deviation 23 Sample Mean 85.74 Sample Size 50 Confidence Level 90% Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Value Interval Half Width 3.2526911935 49 1.6766 5.4533 Confidence Interval Interval Lower Limit Interval Upper Limit 80.29 91.19 Confidence interval for population mean for number of days to sell for western region Data Sample Standard Deviation 45.43 Sample Mean 61.6 Sample Size 50 Confidence Level 90% Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Value Interval Half Width 6.4247722139 49 1.6766 10.7715 Confidence Interval Interval Lower Limit Interval Upper Limit 50.83 72.37 Confidence Interval for Population mean for sales price for western region Data Sample Standard Deviation 26.95 Sample Mean 79.48 Sample Size 50 Confidence Level 90% Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Value Interval Half Width 3.8113055506 49 1.6766 6.3898 Confidence Interval Interval Lower Limit Interval Upper Limit 73.09 85.87 Western Region Eastern Region Western Region OWestern ReWestern RegioEastern Region O Eastern Regi 82 60 20 148 139 140 123 26 103 89 80 70 16 112 100 89 50 72 81 61 135 120 18 136 100 146 143 109 112 89 80 80 79 121 100 125 100 130 83 60 70 60 100 99 80 81 52 96 93 65 103 95 14 98 70 118 100 33 106 100 136 100 101 109 99 101 50 55 102 89 140 75 69 96 96 73 42 120 103 40 135 99 90 84 60 89 40 40 96 50 144 60 130 125 85 109 65 23 136 100 145 100 61 103 103 81 50 133 95 95 136 70 62 149 100 80 80 4 92 88 137 137 101 111 100 102 50 30 108 70 75 42 98 98 68 71 62 189 102 82 109 89 122 109 100 130 119 108 137 137 108 89 19 85 65 146 100 125 94 84 98 80 15 141 141 82 50 7 131 120 79 79 1 130 120 138 99 17 107 80 95 79 23 113 80 136 129 30 142 100 74 34 17 105 60 139 100 25 140 70 143 89 120 83 43 120 109 35 97 90 75 75 25 95 90 136 69 15 129 99 124 132 91 80 54 68 100 69 79 50 54 58 75 25 33 49 100 75 Western Region Sale Price Original Price Mean Median Range Std Dev Minimum Maximum Higher Lower Outlier Higher Lower 107.2 105.5 92 27.85 54 146 79.48 79 109 26.95 34 143 163 51 133 26 93 118 89 73 79 103 Eastern Region Days to Sell Original Price Sale Price 61.6 107.88 85.74 52 103 88.5 188 76 101 45.43 19.52 23.00 1 73 40 189 149 141 152 -29 3 No No 60 100 80 60 60 70 147 69 132 40 4 137, 143 No No 189 No No 137, 139,141 90% confidence Interval 6.27 10.57 79.48+/-6.2761.60+/-10.57 Margin of error in % Sample Size 0.06 40 120 $ % of two means 5.35 85.74+/-5.35 74.14% 89 0.05 43 125 $ 79.48% 99 rn Region Eastern Region Days to Sell 33 59 189 145 91 66 81 65 100 15 34 102 45 166 50 56 53 71 45 80 33 1 23 45 77 20 65 34 144 2 34 45 100 8 10 45 120 100 36 75 69 45 38 56 Western Region Original Price Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Eastern Region Original Price Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 71 34 55 67 78 114 Days to Sell 63.8 56 188 40.77 1 189 145 -18 145, 166, 189 No 9.48 63.8+/-9.48 gion Original Price 107.2 3.9386105496 105.5 80 27.8501822806 775.6326530612 -1.5241005528 -0.0383807245 92 54 146 5360 50 gion Original Price 107.88 2.7601597114 103 103 19.5172764912 380.9240816327 -0.5821283261 0.5115341955 76 73 149 5394 50 Western Region Sale Price Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 79.48 3.8118226397 79 100 26.9536563723 726.4995918367 -0.512088682 0.4229013866 109 34 143 3974 50 Eastern Region Sale Price Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 85.74 3.2521026166 88.5 100 22.9958381328 528.8085714286 0.1635549952 0.3481682227 101 40 141 4287 50 Western Region Days to Sell Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Eastern Region Days to Sell Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count n Days to Sell 61.6 6.424697 52 25 45.42947 2063.837 -0.51554 0.605697 188 1 189 3080 50 n Days to Sell 63.8 5.765343 56 45 40.76713 1661.959 1.243446 1.032431 188 1 189 3190 50