The physicists who announced the likely discovery of the long-sought Higgsboson particle this week were operating according to an extremely high standard of certainty. As was widely reported, in order to achieve discovery status their experiment had to clear a threshold of "five sigmas" of statistical significance. What precisely the five-sigma mark means, however, wasn't always clearly explained in the coverage of a ground-breaking development that could explain how particles have mass and, by extension, why planets and all other objects exist at all. That is partly because the five-sigma concept is somewhat counterintuitive. It has to do with a one-in3.5-million probability. That is not the probability that the Higgsboson doesn't exist. It is, rather, the inverse: If the particle doesn't exist, one in 3.5 million is the chance an experiment just like the one announced this week would nevertheless come up with a result appearing to confirm it does exist. Agency France-Presse/Getty Images In other words, one in 3.5 millions the likelihood of Part of the Large Hadron Collider in Geneva that finding a false positive-a fluke produced by random scientists used to discover the Higgs boson particle. statistical fluctuation-that seems as definitive as the findings released by two teams of researchers at the CERN laboratory in Geneva. The Numbers Guy blog The Particle Proof This is a very high burden of proof as far as science Previously in the Numbers Guy goes. For many medical experiments, researchers need Browser Wars Escalate merely to clear two sigmas. Sigmas don't scale in a Kids Can Be Costly Long After 18 linear way: A two-sigma result can have as much as a Sports Results That Leave Final Score . 5% chance of occurring as a false positive. Three Unclear sigmas, needed to cite evidence-but not discovery-of a new particle in physics, correspond to a one-in-741 chance. Other fields have different benchmarks because less is More on Higgs Boson at stake if a result proves faulty, or, as with pharmaceutical studies, there is more upside to moving ahead quickly with a promising result, statisticians say. "Drugs can be withdrawn, psychological experiments can be refuted, but nobody wants to see the laws of physics proved wrong," says David Spiegelhalter, a statistician at the University of Cambridge. Sigma is the Greek letter used as a symbol for standard Scientists at Europe's CERN research centre deviation-a measure of how far a finding departs from believe they have found one of the basic building blocks of the universe -- a subatomic particle the expected one. The more sigmas attached to a called the Higgs boson. The Director General of result, the more likely it is significant and not due to CERN told an audience of scientists that the discovery is a milestone in mankind's chance. Say a series of experiments on a randomly understanding of nature and has opened up exciting prospects for further revelations in the chosen coin involves flipping it 1,000 times and then field. flipping it 1,000 times again and again. The average number of heads should be 500, but some experiments will yield more and some fewer. A five-sigma finding would be 590 heads. The CERN finding, then, is the equivalent of getting a lot more heads than expected-which is unlikely to occur by fluke rather than for some systematic reason. The best explanation the CERN physicists have for this Physicists said they had discovered a new excess signal is the existence of the long-hunted Higgs particle that is consistent with the Higgs boson, a boson. long-sought particle crucial to scientists' current understanding of how the universe is built. WSJ's Gautam Naik explains its significance. Photo: They set such a high bar to rule out two other possible Getty 1m ages explanations: Either their equivalent of the coin is Discovery May Help Tell Universe's Secrets flawed in a way that tacks on extra positive signals; or 7/4/2012 they've run the study enough times and looked for Physicists Near Clue to Universe 7/3/2012 anomalies in so many places in their data-the equivalent of running the coin experiment over and over with different coins-that they've stumbled upon a seemingly unlikely result just by looking too hard for it. Physicists call this the Look Elsewhere Effect, or LEE, and try to account for it. One CERN group said its findings significance falls to between 4.1 and 4.3 sigmas after accounting for LEE. Another factor can pull in the opposite direction from LEE: when another experiment finds the same thing. That bolsters a findings significance. The Higgsboson was found at the five-sigma level by two CERN experiments. The five-sigma requirement also helps guard against the equivalent of a faulty coin-some kind of measurement error. That appears to be the explanation for a finding last year that certain particles called neutrinos were traveling faster than the speed of light. It now appears to be the result of a flawed cable. Particle physicists cite many examples of results that cleared three but not five sigmas and weren't replicated by follow-up studies, which helped give rise to the five-sigma rule. University of Pisa physicist Giovanni Punzi, who has collaborated on a parallel hunt for the Higgsboson at the Fermi National Accelerator Laboratory in Chicago, says physicists have debated whether the rule is "exaggeratedly high." It was devised decades ago to provide a margin of safety in case calculations of statistics for an experiment, done without today's computing power, were flawed. But counterarguments prevailed: Modern computing power makes it easier to find false positives; and with so many particles discovered, new ones better clear a high bar. Maybe the rule is "not a bad idea, after all," Dr. Punzi says.

Read about the Higgs boson particle from the WSJ (article is above). Using the normal probability density function and the Excel command NORM.DIST to compute the probability of a Type I error. Use the five sigma cutoff point mentioned in the article

Question 6 1 pts Benny operates a gardening service to customers. The services provided include mowing, fertilising, weeding, pruning, garden design and a spring tidy up. The diagram below is used to describe part of the database model used by Just Benny. Refer to the diagram and indicate which of the following statements is TRUE A ' 0 Each service item is for only one customer only 0 An invoice detail is for many customers 0 An invoice can have many invoice details 0 Many customers are included in the one invoice detail Lambda - Arrival Rate (Calls per Minute) Mu - Service Raie(Calls per Minute) Servers 11: Time Server Bus rho Probability of 0.503 0.333 0.1 10 0.030 0.01 2 0.0003 0.00003 In the s stem CUSTOMERS CUSTOMERS CUSTOMERS 0.74 0.07 0.03 0.01 TIME (Minutes) TIME (Minutes) TIME (Minutes) Time in System t(s) Y 4.33 4.38 Time in Line -I Y 0.53 0.03 TIME (Seconds) TIME (Seconds) TIME (Seconds) Time in System I(s) Y 239.7 201 .5 Time in Line I Y 31.7 3.5 Number in System n(s) Number in Line n I Y Y The purpose of this exercise is to discuss the situation facing a manager and help her determine how many servers to use and what the characteristics of the system will be. Endeavor Communications, a long distance provider, is reevaluating its account management department for handling customer service questions and requests. During the 6:00 pm to 10:00pm time period, past data hat calls to the account management department occur at an average rate of one call every 6.5 minutes. A study of past service times indicate that the average time to process a caller's question/request is 4.3 minutes. Like other phone systems, when a call comes in and all the servers are busy, the caller hears a message telling them to hold until the next server is available Top management at Endeavor Communications understands that the staffing decision involves the analysis of trade-offs. Increasing the number of servers will reduce the waiting times and increase the probability of immediate service at a higher cost with more idle time for the servers. Management has decided that the GOAL of the account management department is to immediately answer and service at least 90% of the incoming calls during the busiest time period of 6:00 to 10:00pm. They have asked you to determine the staffing level that will help them meet this goal. Also, they'd like you to provide your own recommendations. 1. What are the arrival and service rates in Calls per MINUTE? Use the spreadsheet to calculate these: A. (calls per minute) = (calls per minute) = 2. Since you are not required to perform the calculations in the case of multiple servers, you are provided with these results in the table that follows. You DO need to determine the information for the case of one server and RHO for 2 and 3 servers, Please fill in the chart below based on the numbers you calculate using your EXCEL FILE which can be found under LabEx Files on the course webpage. USE THREE DECIMAL PLACES IN ALL PROBABILITIES Servers 2 3 % Time Server Busy (rho) Probability of 0.503 0.515 0.333 0.341 0.110 JAWN-O 0.113 0.036 0.025 0.012 0.005 0.0003 0.001 0.00003 0.0003 In the system CUSTOMERS CUSTOMERS CUSTOMERS Number in System n(s) 0.74 0.67 Number in Line n(0) 0.08 0.01 TIME (Minutes) TIME (Minutes) TIME (Minutes) Time in System t(s) 4.83 4.36 Time in Line t() 0.53 0.06 TIME (Seconds) TIME (Seconds) TIME (Seconds) Time in System ((s) 289.7 261.5 Time in Line t() 31.7 3.5 These may be helpful----ONE SERVER FORMULAS: Pa = (1-p)p P. Vu ns= 2/(p=1) ni= p[2/ (H-X)]= phs ts = 1/ (H-1) to= p[1/ (H-X)]=ptsThe owners of an e-business have been successful in selling fashion products but are now venturing into another domain. Knowing that the impact of advertising on profit cannot be overemphasized, they are interested in determining the right amount to allocate to advertising for the new business. Based on a monthly report from the fashion e-business, a regression analysis of monthly profit (in thousands of dollars) on advertising spending (in hundreds of dollars) produced the following results: slope y-intercept 1.34 2.451 0.7372 where y = profit (in $1000s) x = advertising spending (in $100s) a. State the least-squares regression line for the data. 0 + 0 x b. Interpret the value of the slope as it relates to this problem. For every $1 increase in advertising spending, there is a $1.213 increase in profit. O For every $100 increase in advertising spending, there is a $1,213 increase in profit. O For every $100 increase in advertising spending, there is a $121.3 increase in profit. O For every $1,000 increase in advertising spending, there is a $121.3 increase in profit. c. Compute and interpret the coefficient of determination. R- = Round to 4 decimal places d. Predict the monthly profit for a month when advertising is $2,200. $0.00 Round to the nearest cent SAshley's company makes office equipment for both personal home use and office use. Her company spends much more money on advertising in the B2C part of her business rather than the B28 part of the business. Why? A. Publicity is the most effective advertising technique in B2B markets B. B28 marketing is too expensive to use advertising OC. B2B marketing usually involves more personal selling D. B28 markets are too heterogeneous to use advertising OE. Business consumers are more critical of advertising, so it doesn't work as well QUESTION 14 When starting to plan his company's advertising campaign, Haoran first asked, "What appeal should we use?". Why is this a bad first question? A He hasn't determined his target audience O B. He hasn't determined which media he will use C. He hasn't asked which resources he has, such as actors and film equipment O D. Appeals are only used in social media marketing, not in advertising