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For a sample of nine automobiles, the mileage (in 1000s of

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 7E Chapter 5.7

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 7E

For a sample of nine automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to 10% of their original thickness. The results are given in the following table.

Automobile

 Front

 Rear

1

 32.8

41.2

2

 26.6

 35.2

3

 35.6

 46.1

4

 36.4

 46.0

5

 29.2

39.9

6

 40.9

 51.7

7

 40.9

 51.6

8

 34.8

 46.1

9

 36.6

 47.3

Find a 95% confidence interval for the difference in mean lifetime between the front and rear brake pads.

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Step 1 of 3

HARDIK PATNI UMASS BOSTON STUDENT Causes of Environmental Degradation: Market Failures & Policy Failures This is a failure of the two principle allocative mechanisms to allocate resources efficiently. In economics we say that market forces (S & D) will drive the economy to an efficient level of output. However, different circumstances cause market failure: Whenever externalities are present the free market will produce too few positive externalities & too many negative externalities. The free market fails to provide most public goods. When a resource is common property it is overexploited in a free market. When special interests form a coalition and engage in collective action to secure a disproportionate share of benefits. Market Failures 1) Externality: defined as a cost or benefit imposed upon or received by a third party in the production or consumption of a good or service. External costs imposed upon society are not considered in private production decisions. Profits are maximized by producing up to the point where MR = MC; however marginal costs include only private costs. Social costs = private costs + external costs Policy goal is to internalize the external costs, then market allocation will be socially optimal. The real cost of production is the social cost, however because producers do not pay for external costs (external costs are borne by society at large) he ignores them. The profit maximizing rate of output is too high and price is too low because external costs are not accounted for. Failure to pay the “real” or full price for our consumption is at the root of many of our environmental problems. 2) Public goods will not be provided by a free market. Public goods are: Non-exclusive in nature: Once provided they are freely available to all. Hence people will be motivated to act as free riders and resist paying for the public good, even when they value it. No-rivalrous in consumption: One person’s consumption of a pure public good does not affect the amount available for others. 3) Common property or “open access” resources will be over-exploited. HARDIK PATNI UMASS BOSTON STUDENT Open Access: Property rights have not been defined; access and use are free and open (“no man’s land”). For example, forests, pastures, water, fisheries, forest land, and environmental resources. Property rights must be: Well defined Exclusive Secure Indefinite Enforceable Transferable 4) Collective Action: A small special interest, usually with vested economic interests is able to form a coalition and secure benefits for themselves. Most successful when benefits are concentrated and costs are diffuse and most destructive to society. It is very common for special interest groups to proliferate in the U.S. or any stable democracy. 5) Unpriced Resources: Absent or thin markets. Valuable resources are free or undervalued: e.g. clean air, fresh water, biodiversity. Policy Failures 1) Distortion of otherwise well functioning markets (taxes, subsidies, quotas, regulations, inefficient state enterprises or public project of low social return). 2) Failure to consider and internalize the side effects of otherwise warranted policy interventions. 3) Government intervention that aims to correct or mitigate a market failure but ends up making things worse (wrong intervention).S 4) Lack of intervention in failing markets. HARDIK PATNI UMASS BOSTON Note on Price Elasticity of Demand Elasticity: measures responsiveness of one variable to another (determinant). One changes, how does that affect the other Price Elasticity of Demand: A change in price will lead to a change in quantity demanded. Price elasticity will depend on the type of good (luxury or necessity), available substitutes, and how important the price change is (is it noticeable). For higher priced goods a 5% price increase is noticeable, for lower priced it is not (car v. pencil). E d = % change in Q d x/ % change in Price x E d = (change in Q d x/ original Q d x) / (change in P x / original P x) E d = (Q d 2 – Q d 1) / Q d 1 / (P 2 – P 1/ P1) Due to the downward sloping demand curve (inverse relationship) the coefficient E d will always be negative: just take the absolute value. E d > 1 D is elastic E d < 1 D is inelastic E d = 1 Unit Elasticity Price Elasticity of Supply E s = % change in Quantity supplied / % change in Price Cross Elasticity of Demand E xy = % change in Q d x / % change in P y I f positive cross elasticity of demand: Goods are Substitutes HARDIK PATNI UMASS BOSTON If negative cross elasticity of demand: Goods are Complements Income Elasticity of Demand E i = % change in Q d x / % change in Income Coefficient is positive for Normal Goods Coefficient is negative for Inferior Goods HARDIK PATNI UMASS BOSTON Economic Terminology & Definitions  Economics is the study of how scarce resources are allocated among competing claims.  “The Economic Problem” is that human wants are unlimited while resources are limited.  Scarcity of resources (& opportunity cost) is illustrated in economics by the Production Possibility Curve.  A market is an institution or mechanism that brings buyers (demanders) & sellers (suppliers) together.  Market forces (S & D) will push the economy to equilibrium for anything but the very short term. This is stable but not necessarily desirable. If a market is out of equilibrium there will be either a shortage or a surplus.  Demand is a schedule or curve that shows the various amounts of a product that consumers are willing and able to purchase at a series of possible prices during a specified period of time.  “The Law of Demand” = the inverse relationship between Q demanded & P.  Q demanded = f(P-, avail subs -, P of subs +, tastes & preferences +, Y +, # of consumers +, consumers expectations of the future +)  Market demand is the sum of all individual demands.  Change in Demand = a shift of the D curve to right or left in response to a change in one of the determinants of demand.  Change in Quantity Demanded = a movement along the demand curve from one point to another in response to a change in price (the primary determinant).  Supply is a schedule or curve showing the amounts of a product that producers are willing and able to make available for sale at a series of possible prices during a specified time period.  “The Law of Supply” = the positive relationship between Q supplied & P.  Q supplied = f(P +, costs of production -, technology +, taxes - & subsidies +, prices of other goods, price expectations +, # of sellers in the market +)  Market Supply Curve is the sum of all individual producers’ supply curves.  Change in Supply = a shift of the curve caused by a change in one or more of the determinants of supply.  Change in Quantity Supplied is a movement from one point to another along the supply curve due to a change in price. HARDIK PATNI UMASS BOSTON  Consumer Surplus = the difference between maximum willingness to pay and actual price paid (the area under the demand curve and above the equilibrium price), it is the bonus to the consumer.  Producer Surplus = the difference between the minimum amount the producer would be willing to sell goods for and the amount they actually receive (equilibrium price). Producers have different minimum selling prices (or seller’s costs) so they have different surpluses (bonuses).  Total Surplus = Consumer surplus + producer surplus.  Efficiency = cannot make one person better off without making another worse off. At equilibrium price total surplus is maximized.  Price Elasticity of Demand = % change in Q demanded / % change in Price  Price Elasticity of Supply = % change in Q supplied / & change in Price  Income Elasticity of Demand = % change in Q demanded / % change in income. The coefficient is positive for normal goods, negative for inferior goods.  Externality: defined as a cost or benefit imposed upon or received by a third party in the production or consumption of a good or service.  Social Costs = Private costs + external costs  Policy goal is to internalize the external costs, then market allocation will be socially optimal.  Public Goods are: Non- exclusive in nature, once provided they are freely available to all. Hence people will be motivated to be free riders and resist paying for the public good, even when they value it. Non-rivalrous in consumption. One person’s consumption of a pure public good does not affect the amount available for others.  Common Property or “open access” resources will be over- exploited. Property rights have not been defined, access and use are free and open.  Profit maximizing rate of output: Produce where MC = MR  Marginal Revenue = MR = the addition to total revenue for the last unit sold  Marginal Cost = MC = the change in total costs for the last unit produced  GDP = Gross Domestic Product = C + I + G + X – M  C = Consumption  I = Investment  G= Government Spending HARDIK PATNI UMASS BOSTON  X = Exports  GDP can be measured by the sum of all spending or the sum of all incomes  Difference between the Expenditure Approach & the Income Approach is the “Statistical Discrepancy”  Real & Nominal GDP  Real GDP is adjusted for price changes (inflation) for a set Base year  Nominal GDP = current dollars  GDP as a measure of social welfare  N = employment  unN = unemployment  Factors of Production = T, L, K  T = Land  L = Labor  K = Capital  D = Demand  S = Supply  S = Savings  Y = Income  MPC = marginal propensity to consume  MPS = marginal propensity to save  MPC + MPC = 1  a = autonomous consumption  b = MPC  C = a = bYd  T = Taxes  t = tax rate  Yd = Y – tY  Yd = C + S  Fiscal Policy: the use of the tools of the federal government to stabilize the economy or smooth out the business cycle to meet our Macro Policy goals.  Expansionary Fiscal Policy: Increase Government Spending, Decrease Taxes  Contractionary Fiscal Policy: Decrease Government Spending, Increase Taxes  Monetary Policy is conducted by the Federal Reserve, independent of the Federal Government, working through changes in the Money Supply.  Discretionary Fiscal Policy refers to changes in taxes or spending that are the deliberate decisions of the government. HARDIK PATNI UMASS BOSTON  Government Spending Multiplier = 1/1 – MPC = 1/MPS  Tax Multiplier = -MPC/MPS  Balanced Budget Multiplier = 1  The difference between the government’s spending and income (receipts or tax revenue) is the surplus (+) or deficit (-)  Deficit is the current year’s shortfall  Debt is the Total amount borrowed, sum of all deficits – surpluses  U.S. Debt closing in on $17 Trillion  UnN + % of the Labor Force UnN’d  Frictional UnN  Cyclical UnN  Structural UnN  Seasonal UnN  Demand –Pull Inflation  Cost-Push Inflation  Hyper-inflation  Investment=f(r) inversely related  Compare expected Rate of Return (ROR) with interest rate (r)

Step 2 of 3

Chapter 5.7, Problem 7E is Solved
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Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 7E from chapter: 5.7 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: original, brake, pads, rear, thickness. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 7E from 5.7 chapter was answered, more than 422 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “For a sample of nine automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to 10% of their original thickness. The results are given in the following table.Automobile Front Rear1 32.841.22 26.6 35.23 35.6 46.14 36.4 46.05 29.239.96 40.9 51.77 40.9 51.68 34.8 46.19 36.6 47.3Find a 95% confidence interval for the difference in mean lifetime between the front and rear brake pads.” is broken down into a number of easy to follow steps, and 91 words.

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