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In a test to compare the effectiveness of two drugs

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

Solution for problem 5E Chapter 6.5

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 5E

Problem 5E

In a test to compare the effectiveness of two drugs designed to lower cholesterol levels, 75 randomly selected patients were given drug A and 100 randomly selected patients were given drug B. Those given drug A reduced their cholesterol levels by an average of 40 with a standard deviation of 12, and those given drug B reduced their levels by an average of 42 with a standard deviation of 15. The units are milligrams of cholesterol per deciliter of blood serum. Can you conclude that the mean reduction using drug B is greater than that of drug A?

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Chapter 8 ~ Econ 202 ~ Saving, Investment and the Financial System Financial Institutions in the U.S. Economy Section Prelude ~ the U.S. financial system is made up of many types of financial institutions; such as, the bond market, the stock market, banks, mutual funds, hedge funds and venture capitalists. All of these institutions act to direct the resources of households that want to save some of their income into the hands of households and firms that want to borrow. When savings increase, investment increases and thus capital assets increase which in turn eventually leads to economic growth. The financial system consists of the groups of institutions that help to match one person’s saving with another person’s investment. Saving and investment (in regards to GDP) are key ingredients to long- run economic growth and raises a country’s productivity (Y/L) and standard of living.  Financial Markets ~ bonds and stocks (direct exchange for savers and borrowers)  Banks ~ savings accounts and loanable funds (indirect exchange for savers and borrowers)  Mutual Funds ~ indirect (partial, fractional) ownership of companies and bonds in the basket The financial system moves the economy’s scarce (monetary, time, knowledge, etc.) resources from savers to borrowers: This is accomplished via 2 groups of financial institutions: 1. Financial markets ~ bonds & stocks ~ direct exchanges 2. Financial intermediaries ~ banks & mutual funds ~ indirect exchanges Financial markets are the financial institutions through which savers can directly exchange and provide funds to borrowers; such as, the bond market and the stock market. Financial intermediaries are the financial institutions through which savers can indirectly exchange and provide funds to borrowers; such as, the banks and mutual funds. Store of value refers to stocks, bonds, bank deposits that are the accumulation of wealth via savings. A bond is a certificate of indebtedness that specifies the obligations of the borrower to the holder of the bond: A bond is an IOU which specifies the time (date of maturity, term) which the loan will be repaid, the rate of scheduled interest which will be paid to its purchaser and the amount borrowed (called the principle). Bonds are referred to as debt finances for corporations and governments whom use the proceeds for capital investment. When a company encounters financial difficulty, bonds are the first obligation to be paid off to the creditors, because debt needs to be paid off first.  Term ~ is the length of the time of the bond to its maturity. These range in length from a few months to years. A perpetuity bond pays interest for ever but the principle is never repaid.  Credit Risk ~ is the rating on the bond; or its risk of default (junk bonds have higher interest because of higher risks). Credit risk is the possibility that the borrower will fail (default) to pay some or all of the interest or principle associated with that bond.  Tax Treatment ~ is how the bond’s interest is treated in regards to federal income taxes. o Municipal bonds are typically tax-free. Stock ~ represents ownership in a firm, and is therefore, a claim to the profits that the firm makes, and the sale of stock by a company to raise money for capital investment is called equity finance. Stocks carry a higher risk than bonds; however, they potentially produce greater rewards. Their prices reflect the supply, demand and perceptions of that particular company’s future.  Price ~ single most important piece of information about a stock and reflects the company’s true value  Dividends ~ profits paid to stockholders (usually quarterly)  Retained earnings ~ monies NOT paid out and kept for re-investment in corporate capital  Yield ~ is the (annual) dividend divided by the current stock price and reported as a percentage  Earnings per share is the company’s net earnings ÷ by the number of shares in circulation  P/E Ratio (price of the stock divided by earnings per share, indicates risk and value) A stock index tracks a basket of stocks which are grouped together and is a computed average of that group (basket) of stocks. [Dow Jones industrials Average, S&P 500 Index, NASDAQ Composite, NYSE Composite and etc.] For the most part, stock indexes (ETF’s) carry (have) much lower fees and costs than mutual funds because of fewer transactions, because its basket of stocks are pretty much fixed. Banks are the financial intermediaries in which most people have familiarity:  Banks line-up savers (depositors) with investors (borrowers) in an indirect way via savings accounts and loanable funds.  They provide check-writing and debit card services as a medium of exchange for easy transactions.  They provide a store of value; such as, savings accounts and CD’s, for their customers but isn’t as easily accessible as writing checks and swiping debit cards. A mutual fund ~ is an institutional financial intermediary that sells shares, of its fund, to the public and uses the proceeds to buy a portfolio of various stocks and bonds. A mutual fund is very similar to a stock index in which it carries a basket of various stocks and possibly bonds. It varies from a stock index (ETF), because its manager(s) buy and sell (trade) securities within the fund on a regular basis.  The primary advantage is diversification ~ consumers become indirect and partial (fractional) company owners of many different companies at one time.  Secondly, they provide the public with access to professional money managers. An ETF (exchange traded fund) ~ is very similar to mutual funds and stock indexes; however, it trades much more easily in the markets than mutual funds, because a mutual fund is purchased (priced) after the close of the daily market, the ETF can be traded during the day like a stock. An ETF can also function as a stock index fund; such as, the S&P 500’s (SPY) stock index ETF which holds and tracks the same stocks as the parent S&P 500 index. Saving and Investment in the National Income Accounts Section Prelude ~ national income accounting identities reveal some important relationships among macroeconomic variables. In particular, for a closed economy, national saving must equal investment. Financial institutions are the mechanisms through which the economy matches one person’s saving with another person’s investment. Determinant(s) ~ are variables which limits or defines a decision, function or condition: They are the sum formed from the aggregates in accounting identities. Saving & investment are both variables and they are also determinants in regards to a nation’s long-run productivity (Y/L). Variables are quantities that can take on more than one value. Identity ~ is an equation that must be true because of the way the variables in the equation are defined. The equation: Y = C + I + G + NX is an “identity” because every dollar for “Y” shows up in one of the other variables “C + I + G + NX.” Identities clarify how different aggregate variables are related to one another. Accounting ~ refers to how various numbers are defined and added up. Accounting Identity ~ “S = I” ~ is an accounting identity and shows that saving and investment are equal for the economy as a whole; however, it doesn’t have to hold true for every individual household and firm. When S = I, the demand for investment and supply of savings are in equilibrium. An open economy interacts with other economies around the world. A closed economy is one that does NOT interact with other economies; such as, international trade of goods, services, borrowing and lending.  Y = C + I + G (GDP is the sum of only its consumption, investments and government purchases in a closed economy and excludes the NX) Thus, National Saving (saving) ~ is the total income in the economy that remains after paying for consumption and government purchases. This includes the balancing of government taxes minus transfer payments. (T = taxes – transfer payments). The Accounting Identities: GDP = Y = C + I + G (in a closed economy) I = Y - C - G (National Saving, or just saving, private +public saving) S = I (saving = investment: For the closed economy as a whole, saving must be equal to investment.) S = Y - C - G (substitute “I” using “S,” this represents National Saving) S = Y – T – C is Private Saving (disposable income minus consumption ~ income - taxes - consumption) S = T – G is Public (government) Saving (tax revenue - government spending; surplus when tax revenue is greater; a deficit occurs when government spending is greater than tax revenues) Thus, S = (Y – T – C) + (T – G) represents the tax separation of private saving from government saving, and this identity represents national saving (Y – C – G) which also equals “I” (investment). Private Saving ~ is the income that households have left after paying for taxes and consumption. Public Saving ~ is the tax revenue that the government has left after paying for its spending. Budget surplus ~ is an excess of tax revenue over government spending and represents public saving. Budget deficit ~ is a shortfall of tax revenue from government spending. 3 Ways to Remedy the Deficit:  Sell bonds for debt financing  Increase taxes  Cut spending The financial system (bond market, stock market, banks and mutual funds) stands between the two sides of the “S = I” equation and coordinates the market economy via mechanisms behind these identities (equations): When equilibrium occurs, price equals quantity and demand equals supply. Saving ~ when one’s “disposable income” exceeds his/her consumption or expenditures and is what remains after households pay their taxes and pay for consumption:  Personal income = sum of wages, tips, salaries, interest, dividends and other incomes  Disposable income = personal income – federal tax obligations  Private savings = disposable income – consumption (S = Y – T – C) Investment ~ refers to the purchase of new capital; such as, equipment, buildings, a new home and inventories. Investment does NOT refer to the purchase of stocks and bonds of any type. Problem: using: (GDP) Y = C + I + G and GovSavings = T - G and PrivSavings = Y - T- C GDP = $10 trillion, consumption = $6.5 trillion, gov. spending = $2 trillion, deficit = $0.3 trillion Tax Revenue = GovSavings (deficit or surplus) + GovSpending Tax Revenue = $-0.3 trillion (deficit) + $2 trillion = $1.7 trillion Public Savings = Tax Revenue - GovSpending ($1.7 trillion - $2 trillion = -$0.3 trillion) Private Savings = Y - T - C; $10 trillion - $1.7 trillion - $6.5 trillion = $1.8 trillion National Savings = Public Savings + Private Savings = $-0.3 trillion + $1.8 trillion = $1.5 trillion Now assume (suppose) the government cut taxes by $200 billion ($0.2 trillion): 1 Scenario Public Savings = $-0.3 trillion - $0.2 trillion = -$0.5 trillion (deficit increased 66.67%) Tax Revenue = $-0.5 trillion (deficit) + $2 trillion = $1.5 trillion (tax revenue decreased 11.67%) Private Savings = Y - T - C; $10 trillion - $1.5 trillion - $6.5 trillion = $2 trillion (increased 11.1%) National Savings = Public Savings + Priv. Savings = $-0.5 trillion + $2 trillion = $1.5 trillion (no change) Scenario # 2 ~ if consumers spend ¾ of tax-cut and save ¼ of tax-cut: 0.75 x 0.2 trillion = $0.15 trillion; consumption would be $6.5 + $0.15 = $6.65 trillion Private Savings = Y - T - C; $10 trillion - $1.5 trillion - $6.65 trillion = $1.85 trillion (2.78% increase) Nat. Savings = Gov. Savings + PrivSavings = $-0.5 trillion + $1.85 trillion = $1.35 trillion (10% decrease) The effect of a tax cut on the national saving depends on the behavior of the consumers…. The Market for Loanable Funds ~ is the flow of resources available to fund private investment: Section Prelude (1) ~ the interest rate is determined by the supply and demand for loanable funds. The supply of loanable funds comes from households that want to save some of their income and lend it out. The demand for loanable funds comes from households and firms that want to borrow for investment. To analyze how any policy or event affects the interest rate; one must consider how it (the policy or event) affects the supply and demand for loanable funds. Section Prelude (2) ~ national saving equals private saving plus public saving. A government budget deficit represents negative public saving, and therefore, reduces national saving and the supply of loanable funds available to finance investment. When a government budget deficit crowds out investment, it reduces the growth of productivity (Y/L) in GDP. Market for loanable funds ~ is that market in which those who want to save, supply funds, and those who want to, borrow to invest, demand funds.  Loanable funds ~ are the incomes left over after one’s consumption that people have chosen to either save or to loan out to investors whom have chosen to use to invest in new projects.  Saving is the source of the supply of loanable funds ~ all savers deposit their funds in this market. (The opportunity cost of “holding cash” is the forgone interest that could be earned).  Investment is the source of the demand for loanable funds ~ all borrowers take out loans from this market. (Firms borrow for equipment & building; households borrow for new houses).  The interest rate is the price of the loan which lenders receive and borrowers pay ~ there is one interest rate which is both the return on saving and the cost of borrowing.  The supply of loanable funds comes from National Saving which is the sum of public and private saving. The real interest rate is the nominal interest rate corrected for inflation and more accurately reflects the real cost of borrowing and the real returns on lending. Saving represents supply and investing represents demand. Saving is a long-run determinant of productivity (Y/L) which defines a country’s standard of living. The low rate of saving in the US is partly due to tax laws which discourage saving. Government policies affect savings via 3 policies:  Saving Incentives ~ taxes on interest erode savings substantially over time; and saving incentives increase the supply of loanable funds for re-investing because of lower interest rates  Investment Incentives ~ (investment tax credit) ~ firms would be encouraged to invest more which would lead to higher interest rates which would in turn lead to greater saving  Government Budget: 1. Government deficit is an excess of government spending over tax revenue 2. Government debt is the accumulation of prior borrowing 3. Government surplus is an excess of tax revenue over government spending 4. A balanced budget occurs when spending is equal to revenues Crowding Out ~ is a decrease in investment by households or firms as a result from excessive government borrowing which shifts the supply curve to the left and increases interest rates. When the government reduces national saving (S = Y – C – G) by running a budget deficit, the interest rate rises and investment falls. This in turn reduces the nation’s long-run growth rate. Loanable Funds ~ refers to the flow of resources available (to fund) private investment. The government’s budget deficit reduces the supply of loanable funds because of increased interest rates. The Supply & Demand curves of Interest rates to the Loanable funds due to government policies: 1. Which curve would a government policy affect 2. Which way does that curve shift 3. How does the equilibrium of the interest rate and quantity of loanable funds change Saving shifts the supply curve to the right; whereas, decreased saving shifts the supply to the left. Government borrowing and government budget deficits shifts the supply curve to the left ~ because “loanable funds are the flow of resources available to fund (private investment).” Thusly, budget surpluses shift the supply curve to the right. Private and business borrowing shifts the demand curve to the right. Interest rate change causes the movement along the supply and/or demand curves. Investment (borrowing) and saving (depositing) are responsible for supply and demand curve shifts. Investment is important for long-run economic growth and a nation’s standard of living. When people save more, the supply curve moves to the right. Which in turn increases the quantity of loanable funds saved and invested, then the equilibrium interest rate would fall and stimulate investment (borrowing). When the demand for loanable funds increase because of tax credits, the demand curve shifts to the right and the equilibrium interest rate increases which stimulates the quantity of loanable funds saved and invested. Government deficits and borrowing shifts the supply curve to the left, lowers the national savings, decreasing the supply and quantity of loanable funds, the increased interest rate thusly “crowds out” potential borrowing by households and firms. The Debt-to-GDP Ratio and Debt Financing Because GDP is a rough measure of the government’s tax base, a declining debt-to-GDP ratio indicates that the government indebtedness is shrinking relative to its ability to raise tax revenue. A rising debt-to-GDP ratio indicates that the government indebtedness is increasing relative to its ability to raise tax revenue. War is usually a government’s cause in fluctuations in debt-to-GDP ratio.  Debt financing allows the government to keep tax rates “smooth, buffered” over time  Shifts part of the costs to future generations by linking the present to the future Debt-to-GDP (Debt/rGDP) increases because of: Note that: rGDP = Y = T – G  Recessions  Tax cuts that are signed into law  Increases in government spending The price (interest) of loanable funds is governed by the forces of supply and demand; just like, the “invisible hand” does with other prices for goods and services in the economy. When financial markets bring the supply and demand for loanable funds into balance (equilibrium, price = quantity and S = I), they help allocate the economy’s scarce resources to their most efficient uses by organizing their economic activities. CHAPTER 8 REVIEW & SUMMARY OF QUICK NOTES Debt finance is the sale of bonds to raise funds. Equity finance is the sale of stock. When a firm encounters financial difficulty, the firm is obligated to pay off bondholders before giving anything to stockholders. Stockholders, however, stand to gain more if a firm is profitable. Corporations issue stock to raise money, a practice known as equity finance. Each share of stock represents partial ownership of the company, so investors' perceptions of the company's future profitability is reflected in the price of the firm's stock. The price of a stock is determined by the forces of supply and demand. If people expect a corporation to have unusually high profits in the future, demand for the stock increases, and its share price rises. A stock index represents an average of a group of stock prices. If optimism about corporate profits is economy-wide, we would expect the major stock indexes, such as the Dow Jones Industrial Average or the Standard and Poor’s 500, to increase. An increase in the number of shares of stock a company issues represents an increase in the supply of the shares—it will reduce the value of each share since the value of the company is split into smaller units. A firm can raise money only through the initial offer of its shares. Once the shares begin trading among stockholders on organized stock exchanges (like the New York Stock Exchange), the proceeds from selling a stock accrue directly to the stockholders. A bond's term—the length of time until maturity—affects the interest rate on the bond. Short-term bonds are less risky than long-term bonds because the bondholders receive the principal payment sooner. To compensate for the additional risk associated with waiting longer for repayment, long- term bonds tend to offer higher interest rates. A closed economy does not trade with the rest of the world, and, thus, its net exports are zero. National saving is the total income in the economy that is left over after paying for consumption and government purchases. In a closed economy, subtracting consumption and government purchases from GDP also yields investment spending, so national saving equals investment. Private saving is the income that remains after households pay taxes and make consumption expenditures. When a government spends less than it collects in tax revenues, it runs a government budget surplus. Public saving is positive in the case of a budget surplus. Note that national saving can be thought of as the sum of private and public saving. National saving is what's left over after you subtract household consumption and government spending from the economy's total income. At the household level, saving is what's left over after subtracting taxes paid and consumption from household income. Depositing unspent income in a bank is an act of saving, as is using unspent income to purchase stocks or bonds. Investment is spending on new capital, such as machines, equipment, tools, or buildings. Also note that spending on new residences is the one component of household expenditures that counts toward investment spending, rather than consumption, in national income accounting. The demand for loanable funds comes from households and firms that want to finance investment spending by borrowing. A household purchasing a new home or a business purchasing new capital equipment might pay for the expenditure by borrowing in the market for loanable funds. The interest rate represents the cost of borrowing money to finance investment expenditures. The demand for loanable funds curve slopes downward. Households and firms will want to borrow a larger quantity of loanable funds at lower interest rates, and a smaller quantity of loanable funds at higher interest rates. Based on a graph, at the interest rate of 4.5%, the quantity of loanable funds supplied ($450 billion) is less than the quantity of loanable funds demanded ($550 billion), resulting in a shortage of loanable funds. Because of the shortage, lenders will find that they can safely increase the interest rates they charge. As they do so, the return to saving rises, and the quantity of loanable funds supplied will increase. At the same time, the higher cost of borrowing prices some borrowers out of the market, and the quantity of loanable funds demanded declines. This process continues until the interest rate reaches the equilibrium level of 5%, where the quantity of loanable funds demanded is exactly equal to the quantity of loanable funds supplied. Saving is the source of the supply of loanable funds. Reducing the level of saving that households can shelter from income tax will discourage saving at each interest rate, causing the supply of loanable funds to shift to the left. There is a shortage of loanable funds at the initial interest rate. With more willing borrowers than lenders, the lenders will be able to raise the interest rate they charge for loans. As the interest rate rises, the quantity of loanable funds demanded decreases. The equilibrium interest rate rises, and the equilibrium quantity of loanable funds saved and invested falls. The implementation of the new investment tax credit will encourage firms to invest more at every interest rate. The policy causes the demand for loanable funds to shift to the right. There is a shortage of loanable funds at the initial interest rate. With more willing borrowers than lenders, the lenders will be able to raise the interest rate they charge for loans. As the interest rate rises, the quantity of loanable funds supplied increases. The equilibrium interest rate rises, and the equilibrium quantity of loanable funds saved and invested rises. The government moves from a budget balance to a budget surplus when it reduces government spending without changing taxes. This increase in public saving causes national saving to rise. Since saving is the source of supply in the market for loanable funds, the increase in public saving causes the supply of loanable funds to shift to the right. The result is a surplus of loanable funds at the initial interest rate. As lenders lower their interest rates to attract borrowers, the quantity of loanable funds demanded increases. The equilibrium interest rate falls, and the equilibrium quantity of loanable funds saved and invested rises. Crowding out is the reduction in the level of investment that occurs when the government borrows to finance a budget deficit.

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Chapter 6.5, Problem 5E is Solved
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Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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In a test to compare the effectiveness of two drugs