In a study of the effect of cooling rate on the hardness of welded joints, 50 welds cooled at a rate of 10 ºC/s had an average Rockwell (B) hardness of 91.1 and a standard deviation of 6.23, and 40 welds cooled at a rate of 30°C/s had an average hardness of 90.7 and a standard deviation of 4.34.
a. Find a 95% confidence interval for the difference in hardness between welds cooled at the different rates.
b.Someone says that the cooling rate has no effect on the hardness. Do these data contradict this claim? Explain.
Chapter 1: Principles of Economics What is economics Economics is the study of how society manages its scarce resources. How do we use graphs in economics We graphs to illustrate the relationship between variables. The following illustrates the negative relationship between price and quantity. As the price decreases the quantity increases – this is a negative relationship because the quantity slope is negative. Economics • Scarcity of resources (income, time, natural resources) ◦ Unlimited wants and desires ◦ Choices • Social Science of individuals choice behaviour, given you have scarce resources. Three Economic Ideas (Assumptions that we make) 1. People are rational – they use information to make a rational choice. 2. People respond to incentives, 3. Optional decisions are made at margin (one additional unit). Four Principles of Individual Decision Making 1. People face trade-offs. 2. Opportunity Cost (something that you give up to gain something). 3. Rational people think at the margin. 4. People respond to incentives. How People Interact 1. Trade can make everyone better off. • Specialization 2. Market (Buyer and Seller) – the exchange of goods and services. • Invisible Hand 3. Government Role • Property Rights • Prevents Market Failure • To avoid externality How does the Economy Works (a) Standard of Living • Depends on its ability to produce goods and services • Gross Domestic Product (GDP) -- $ • Price x Quantity • Better Productivity – better GDP (b) Price rises when the government prints too much money • Inflation – purchasing power does down and impacts standard of living. (c) Trade-off between inflation and unemployment • As inflation increases the rate of unemployment goes down. • The reason that this happens is because a firm will want to produce more goods at the hire price and thus will hire more workers to produce that quantity. Two Types of Statements 1. Normative Statements • What is (fact) • Heart Disease is the leading illness that kills 1 out 3 people everyday. 2. Positive Statements • Should (Policy) • The government should increase taxes on cigarettes. Chapter 2: Thinking Like an Economist Creating an Economic Model Asimplified version of reality 1. Assumptions are decided to use when developing a model. The following list is an example of assumptions made: ➢ Rational/Work Ethic ➢ Same experience ➢ Similar work performance ➢ Same state 2. Atestable hypothesis is made. ➢ The higher the education level the better Illustration 1: Economic Model of Education wages are earned. and Wages 3. Economic Data is used to test the hypothesis. ➢ Surveys, census data, etc. 4. The model is revised if it fails to explain economic data well. 5. Retain the revised model and use for similar experiment. Models 1. Circular Flow Diagram (See Illustration 2) • Illustrates the flow of money and resources. • Two types of market ➔ Product Market ➔ Factor Market (Land, Labor, Capital) Illustration 2: Circular Flow Diagram 2. Production of Possibilities Frontier (PPF) • Illustrates Trade-Off ➔ Frank can produce 32 pounds of potatoes in 8 hours or he can produce 8 pounds of meat in 8 hours. The illustration to the left displays his production possibilities frontier. ➔ Apoint within the PPF is feasible but is inefficient. ➔ Apoint on the PPF is optimal. ➔ Apoint outside of the PPF is not Illustration 3: PPF of Meat and Potatoes feasible. • The PPF also illustrates the opportunity cost ➔ For Frank, the opportunity cost of 1 lb of potatoes is ¼ lb of meat and the opportunity cost of 1 lb of meat is 4 lbs of potatoes. Chapter 3: Gains from Trade Scarcity of resources leads to trade-off which leads to making choices with the highest benefit. With trade, we don't face trade-offs. Productions Possibilities Frontier Frank is able to produce 1 pound of potatoes every 15 minutes or 1 pound of meat every 60 minutes. Rose is able to produce 1 pound of potatoes every 10 minutes or 1 pound of meat every 20 minutes. The following table illustrates their production of meat and potatoes in an 8 hour day. Potatoes Meat (pounds) (pounds) Frank 32 8 Rose 48 24 Using the information from the table above we can create their production possibilities frontier. Illustration 2: Frank's Production Possibilities Illustration 1: Rose's Production Frontier Possibilities Frontier Now, lets say that Rose talks to Frank about trading so that they can specialize in producing the good that they are best at producing. Frank is not sure of which good he is good at producing. Rose explains that his opportunity cost of producing 32 pounds of potatoes is 8 pounds of meat. Thus, his opportunity cost of producing 1 pound of potatoes is ¼ pounds of meat. She also explains that her opportunity cost of producing 48 pounds of potatoes is 24 pounds of meat. Thus, her opportunity cost of producing 1 pound of potatoes is ½ pounds of meat. After explaining that person who has the lowest opportunity cost of producing potatoes should specialize in producing potatoes. Frank and Rose reach an agree that Frank will produce potatoes and Rose will produce meat. In exchange for 5 pounds of meat, Frank will give Rose 15 pounds of potatoes. The following table displays their consumption of potatoes and meat before trade and after trade. With trade, both Frank and Rose are able to reach a point outside of their original production possibilities frontier. There are two definitions that we should know at this point – absolute advantage and comparative advantage.Absolute advantage is the ability to produce a good or service using fewer inputs than the other producer. In our example, Rose has the absolute advantage in producing both potatoes and meat because it takes her less time to produce both meat and potatoes than Frank. Comparative advantage is the ability to produce a good at the lower opportunity cost than the other producer. In our example, Frank has the comparative advantage in producing potatoes and Rose has the comparative advantage in producing meat.