Answer each question with at least 150 words each. Make sure to include references at the end of each answer.
Question 1. In six sentences or more, explain how you would use descriptive statistical procedure(s) at work or in your personal life.
Question 2. As we will see in the next 12 weeks, statistics when used co
ectly can be a very powerful tool in managerial decision making.
Statistical techniques are used extensively by marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, etc...
As such a strong tool, statistics is often misused. Everyone has heard the joke (?) about the statistician who drowned in a river with an average depth of 3 feet or the person who boarded a plane with a bomb because "the odds of two bombs on the same plane are lower than one in one millionth".
Can you find examples in the popular press of misuse of statistics
Question 3. There are 23 people in this class. What is the probability that at least 2 of the people in the class share the same birthday?
Question 4. Let’s say you are a contestant on a game show. The host of the show presents you with a choice of three doors, which we will call doors 1, 2, and 3. You do not know what is behind each door, but you do know that behind two of the doors are beat up 1987 Hyundai Excels, and behind one of the doors is a
and new Cadillac Escalade. The cars were placed randomly behind the doors before the show, and the host knows which car is where. The way the game is played out is as follows. The host lets you choose a door. Assume you choose door #1. Before he opens door #1 to let you see what you have chosen, he opens one of the remaining doors, say door #3, to reveal a Hyundai Excel (he will always open one of the remaining doors that has the booby prize), and asks you whether or not you want to change your choice to door #2. What do you tell him?
Question 5. Operations and production managers often use the normal distribution as a probability model to forecast demand in order to determine inventory levels, manage the supply chain, control production and service processes, and perform quality assurance checks on products and services. The information gained from such statistical analyses help managers optimize resource allocation and reduce process time, which in turn often improves profit margins and customer satisfaction.
Based on your understanding of the characteristics of the normal distribution, examine the chart below. Process A standard deviation is .9, Process B standard deviation is 1.4, and the mean of both processes is 12. Contribute to our discussion by posting a response to ONE of the questions below.
1. Do either of the processes fit a normal distribution? Why or why not?
1. Which of the processes shows more variation? What does this mean practically?
1. If the product specification quality limits were 12 +/- 3, which of the processes more consistently meets specification? Explain why.
1. If the product specification quality limits were changed to 12 +/- 6, is quality loosening or tightening? Which process would benefit the most from this change?
1. Are there processes at your place of employ that you believe follow a normal distribution? If so, describe one. Why do you believe it is normal?
Question 6. Check out this snippet from Family Circle magazine (January, 2009, Liz Plosser):
Motorists who talk on a cell phone while driving are 9% slower to hit the
akes, 19% slower to resume normal speed after
aking and four times more likely to crash.
Interesting, eh? Need more information? So
y, that's all the information this article provided. So, what can we conclude? How reliable are these results? Can you believe what the author tells you? Why or why not?
Pretend you're a manager for one of the major cell phone service providers in the U.S. You've been asked by a major news magazine to speak to these "accusations." What would you say? Use your knowledge of "statistics for managers" to level some well-founded criticisms of the conclusions above.
Careful! We cannot use personal opinions to battle statistics like these! Instead, you must explain why the numbers reported in Family Circle may, or may not, accurately represent the population of U.S. drivers. There are 100 possible answers to this conference topic.
Question 7. Statistically speaking, we are generally agnostic to which is a bigger problem, type I (false positive) e
ors or type II (false negative) e
ors. However, in certain circumstances it may be important to try and put more emphasis on avoiding one or the other. Can you think of an example of where you may want to try harder to avoid one type or another? Can you think of a policy; political, economic, social, or otherwise, that pushes people toward avoiding one type or another? What are the repercussions of such policies?
Question 8. Many of you will have heard of Six Sigma management. What you may not realize is that the etymology of the term Six Sigma is rooted in statistics. As you should have seen by now, statisticians use the Greek letter sigma (σ) to denote a standard deviation. So when these Six Sigma people start talking about “six sigma processes,” what they mean is that they want to have processes where there are (at least) six standard deviations between the mean and what would be determined to be a failure. For example, you may be examining the output of a factory that makes airline grade aluminum. The average tensile strength of each piece is 65 ksi, and you view a particular output as a failure if the tensile strength is anything less than 64 ksi. If the standard deviation is less than .166, then the process is six sigma. The odds of a failure within a six sigma process are 3.4 in a million, which co
esponds to the XXXXXXXXXX% confidence level. When we are doing statistics, we usually use the 95% confidence level, which is roughly 2 sigmas.
In the case of the tensile strength of airline grade aluminum, 6 sigmas is probably a good level to be at—catastrophic failure on an airplane could open you up to lawsuits worth billions of dollars. But there are some other processes that you probably don’t need to be so certain about getting acceptable products from. Give some examples from your own business life of random processes that are likely to be normally distributed and say how many sigmas you think the process should be at.
Question 9. Test-preparation organizations like Kaplan, Princeton Review, etc. often advertise their services by claiming that students gain an average of 100 or more points on the Scholastic Achievement Test (SAT). Do you think that taking one of those classes would give a test taker 100 extra points? Why might an average of 100 points be a biased estimate?
Question 10. A few random results for you to ponder…do the results justify the conclusions? Why or why not? Pick one or two statements and comment.
In the NFL, teams win more often when they score 13 points than when they score 14. Thus, scoring points is bad.
Often when people use regression analysis to estimate the effect of police officers or police spending on crime, they find that cities with larger police forces
udgets have higher crime rates. Therefore, police cause crime.
As ice cream sales increase, so do drowning deaths. Thus, ice cream causes people to drown.
Studies find that students who drink more tend to have lower grades. Therefore, drinking leads to poor student performance.
Over the past 300 years, there has been a decrease in the number of pirates on the high seas, along with an increase in average global temperatures. Thus, the reduction in piracy has led to global warming.
Did you know there is a health benefit to winning an Oscar? Doctors at Harvard Medical School say that a study of actors and actresses shows that winners live, on average, for four years more than losers. And winning directors live longer than non-winners.
Children who come further down in the birth order have, on average, lower IQs than those born earlier in the birth order (e.g. First born children vs. 5th born children). Therefore birth order determines intelligence.