H ADM 201: Homework IX Due 2:00 pm Friday, April 28 2006 Name:_____________________________________________ Please check your recitation section in the space provided below: H ADM 201, Section 1. (Mondays 4:40 PM: Michelle Tong) H ADM 201, Section 2. (Mondays 7:40 PM: Michelle Tong) H ADM 201, Section 3. (Tuesdays 4:40 PM: Melanie Pope) H ADM 201, Section 4. (Tuesdays 7:40 PM: Melanie Pope) This cover page must be stapled to the homework you turn in. It is the front page of your homework. Make sure to fill out the information requested above. GRADING SHEET MAXIMUM SCORE SCORE EARNED H ADM 201 Homework IX Spring 2006 Question 1. Midway through the oft-delayed construction of the new Starbucks in Ithaca, <a href="/keyword/corporate-headquarters/" >corporate headquarters</a> in Seattle changed the design of new stores in order to eliminate bottlenecks in the ordering process. They claim that the new design is especially efficient during peak periods, and therefore, as more orders are made, more total time is saved. In order to convince the store owner that it is worth further delaying the project and the additional costs, they send a data file showing the total amount of orders placed during any 4 hours during peak-periods and the change in the average amount of time it took to process those orders from a store with the older design. Data appears in Hwk9Q1DatSp06. Unless otherwise stated, use = 0.05 or 95% confidence level, where applicable. A. Does the new system save time over the older system as the number of orders increases (state the hypotheses, compute the test statistic and corresponding pvalue, and state conclusions)? B. What is the likelihood that the new system reduces mean order processing time by more than one minutes per order (state the hypothesis, compute the test statistic and p-value, and state conclusion)? C. What is the likelihood that the new system reduces mean order processing time by less than 0.5 minutes per order (state the hypothesis, compute the test statistic and p-value, and state the conclusion)? D. If you expect the get about 100 orders during peak periods, how much total time saving would there be over the old system if you redesigned? (Be sure to give your answer in an &quot;inferential&quot; fashion.) E. State and interpret the r2 for this regression. F. Using information from the regression output, show how you would calculate the r2 if you were not given the value. Why does the formula for r-squared give the interpretation to this statistic that it does? G. Note that 1-r2 = SSE/SSTo. Compute and interpret this statistic. Explain why this formula gives the interpretation to this statistic that it does. H. Using the regression output, estimate the variance around the regression line. I. Is ,,number of orders a significant (linear) predictor of change in order time (state the hypothesis, find the test statistic and p-value, and state conclusion)? J. Interpret the F-statistic from the ,,Analysis of Variance table in the output. What does this statistic test? What conclusions can we draw from it? 2 H ADM 201 Homework IX Spring 2006 Question 2. You are the manager of the local Hampton Inn in Ithaca. Hilton Corporate recently contacted you, telling you about their new room amenities package (a nightly expense). However, you are very concerned with ROI for each dollar since raising debt servicing costs are squeezing your net profit numbers. The representative from Hilton tells you that for each dollar invested in the new packages, nightly revenue should increase by $1.21. To back this claim up, Hilton sends you data from 25 properties that have already committed to the upgrades. The data file shows change in nightly revenue from a 3 month period before investing and the amount invested (in hundreds of dollars). They run a regression and report the output to you: Change in Nightly Revenue = - 2.06 + 1.23 Amount Invested per Night Would you invest money in this investment strategy? Explain fully. Your answers to the following problem should contain the following elements: A. Formulation of the analytical objective and defense of your choice of the appropriate inferential technique (interval estimate, hypothesis test, significance test) used to reach this objective. B. Notation for the random variable(s) and parameter(s) of interest; define these explicitly. Give the distributional assumptions for your random variable(s) and state all assumptions necessary for the statistical application you intend to use. C. Calculations for the analysis. For hypothesis and significance tests, formulate the null and the alternative hypotheses and calculate the value of your test statistic, as well as the p-value. For confidence intervals, show the appropriate formula. Computer printout should be included here if relevant. D. Draw statistical conclusions from your analysis (this should be brief). E. A discussion of whether the assumptions are met sufficiently closely for the validity of the statistical inferences; use graphs, and other tools where applicable. F. Discuss the sampling scheme and whether or not it is sufficient to meet the objective of the study. Be sure to include whether or not subjective inference is necessary and if so, defend whether or not you believe it is valid. G. In terms lacking statistical vernacular (vocabulary), describe your results as you would to a layman without any statistical training. Be sure to include limitations of the sampling scheme, if any exist. Please label each part of your solutions as shown above whenever applicable. Unless otherwise stated, use = 0.05 or 95% confidence level, where applicable. 3 H ADM 201 Homework IX Spring 2006 Question 3. The Singapore government is concerned with maintaining the regional competitiveness of the city-state as a major tourist destination. Gambling has always been very popular in Asia, and as the Chinese economy increases its ability to send foreign tourists (rising by millions every year) they feel that it is increasingly important to offer world-class gaming resorts on par with ones already built in Australia, Macau, Monaco, and the United States. However, Singapore has a world image of being one of the cleanest, safest, strictest, and best organized cities, and the government is worried that these major gambling facilities might hurt that image. The government board in charge of approving the projects asks major local developers for evidence the benefits of casinos to the local economy. The team gathers data from major gaming destinations around the world showing the number of casinos that opened in any particular year and the change in total tourist traffic from the year before the casinos opened. If the Singaporean government is considering granting two licenses, how many more tourists can they expect in the first year? Data appear in Hwk9Q3DatSp06. 4