New (min) 420 800 765 900 1200 1200 980 456 909 980 1100 1004 420 1100 900 850 1100 1100 900 1100 New ($) 140 266.67 255 300 400 400 326.67 152 303 326.67 366.67 334.67 140 366.67 300 283.33 366.67 366.67 300 366.67 Old (min) Old ($) 180 200 202 145 200 130 110 90 80 190 230 101 180 90 80 88 90 90 80 90 60 66.67 67.33 48.33 66.67 43.33 36.67 30 26.67 63.33 76.67 33.67 60 30 26.67 29.33 30 30 26.67 30 Time Line 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 15 15 15 18 18 18 21 21 21 15 15 15 18 18 18 21 21 21 15 15 15 18 18 18 21 21 21 Downtime 23 20 21 22 19 20 19 18 21 22 20 19 24 25 22 20 19 22 18 18 16 21 23 20 20 22 24 Mech Skill L L L L H L H H L L L H L L L H H L H L H L H L H H L 1. When performing a regression analysis it's important to look at the residual model diagnostics. For each of the following residual plots, what should you look? a. Normal probability plot b. Residuals vs. the fitted values c. Histogram d. Residuals vs. the order of the data 2. Your company introduced several new accessories for their top selling consumer product last quarter. Each accessory has a different price point. You want to determine if the cost is a good predictor of sales. Perform a correlation and regression analysis to determine the statistical relationship between the cost per item and the number sold. Attach the output of your analysis. Include the conclusions drawn from the results of the analysis. Accessory A B C D 3. No. Sold 5541 2949 884 865 Cost per Item 15 10 9 5 A company develops a next generation product line, but does not design it to six sigma capabilities. The next generation results in a lot of defects and variation that is ultimately passed onto the customer. The customers experience a lot of in-field defects causing them \"heart burn\". The number and length of calls into technical support increase for the next generation dramatically, thereby costing the company a lot more money. Based on the data (Analyze challenge Data.xls - Next gen product line tab), answer the following questions and attach the output of your analysis. a. Perform a correlation and regression analysis to determine the statistical relationship between the increase length of call and the cost to the company. b. Determine the difference in the relationship between the cost to the company with the new product versus the cost to the company with the old product. Comment about the difference. c. What other analytical tools do you recommend to determine if there is a significant difference that the new product is costing the company versus the old product? Explain why and how the tools would determine if there is a statistical significance. d. Based on these results, what are your next steps as the project leader? 4. Your department has 5 operators on one assembly line producing the same product. Each has different levels of experience. Defect data from the past month is summarized below. Is there a statistically significant difference in the number of defects between operators? # Defects # Good Operator 1 10 150 Operator 2 8 155 Operator 3 15 160 Operator 4 10 163 Operator 5 8 160 1 Conduct the appropriate hypothesis test and attach the output of your analysis. Include the conclusions drawn from the results of the analysis. Based on your results, what are the next steps? 5. Customers place orders via customer service rep or on-line (electronically). The orders and the total number of successes (or \"error free\" orders) were tracked for the past 6 months. The results are below. Is there a statistically significant difference in errors between orders placed via CSR versus electronically? Orders CSR # Success Orders Electronically # Success 1222 1200 1576 1570 1101 1100 1203 1101 1120 1099 1304 1268 1298 1201 1290 1245 1280 1200 1275 1200 1178 1175 1203 1197 Answer the following: a. Ho = b. Ha = c. Type of data = d. Type of analysis = e. Confidence level and risk = f. Conduct the appropriate hypothesis test and attach the output of your analysis. Include the conclusions drawn from the results of the analysis. Based on your results, what are the next steps for this project? 6. Correlation and regression determines the relationship between 2 variables, but the output does not determine statistical significance. Answer True (T) or False (F) 7. The higher the R squared value, the less the statistical relationship. Answer True (T) or False (F) 8. A scatter plot also determines statistical significance between two variables. Answer True (T) or False (F) 9. What does the confidence level determine (in simple terms)? 10. Determine the risk for each of the confidence levels below: Confidence Level risk 95% _____ 90% _____ 80% _____ 99% _____ 11. If the confidence level is 90% and the p-value is 0.08, what conclusions can you draw? 12. Chi square testing is used with ______ (attribute or variable) data and ____ sample size. 2 13. Identify 3 advantages and 3 disadvantages of EVOP 14. A rancher wants to estimate the average weight gain of cattle he takes to market. He selects a sample of 16 cattle. What is his confidence interval for weight gain? 221 284 245 254 239 182 298 290 272 259 271 239 237 259 210 211 15. Tire Mart receives a shipment of 100 tires from a manufacturer. Within 3 months they receive 7 tires back as defective. The over head of replacing a tire is $18. How much should they budget to cover the maximum cost of potential claims for their next order of 100 tires from this manufacturer? 16. Your department has 3 assembly lines and recently has had a problem with machine downtime. Using the data (Analyze Challenge Data.xls - Confidence Int Downtime tab), answer the following questions and attach the output of your analysis. Include the conclusions drawn from the results of the analysis a. Find the confidence interval on downtime. b. Find the confidence interval on the variance. c. Run an ANOVA (GLM) on the data set below. Is there a significant factor? 17. A survey was conducted to determine if there is a difference in customer satisfaction levels by region. The survey responses were satisfied, dissatisfied or neutral. A Chi square analysis for 5 regions shows there was is not a statistically significant difference in customer satisfaction by region. However the p- value is 0.076 so you decide to do further analysis. Complete the table below. What conclusions are drawn from the results? (df = 2) Region A B C D Chi square Total 0.252 4.614 3.715 2.842 Cum Prob P value 18. A supplier claims an improvement in part diameter from a new machining process. The average diameter is 33.5 (compared to 36.5 from the old process) with a standard deviation of 1.02. How many samples are needed to validate this claim? Acceptable test risks are 5% alpha and 10% beta. 19. One of your key customers has complained that 5% of the orders received are incorrect. You've changed the customer order process to reduce incorrect orders to 1%. How many orders will you need to look at to detect this improvement? 3