Explain why the question T: Type of data—one variable or two? Categorical or numerical? is one of the four key questions used to guide decisions about what inference method should be considered.
> Consider the following statement: The proportion of all students enrolled at a particular university during 2017 who lived on campus was 0.21. a. Is the number that appears in boldface in this statement a sample proportion or a population proportion? b
> Consider the following statement: An inspector selected 20 eggs at random from the eggs processed at a large egg production facility. These 20 eggs were tested for salmonella, and the proportion of the eggs that tested positive for salmonella was 0.05.
> Explain why there is sample-to-sample variability in pˆ but not in p.
> Consider the following three relative frequency histograms. Each histogram was constructed by selecting 100 random samples from a population composed of 40% women and 60% men. For each sample, the sample proportion of women, pˆ, was calculated
> A random sample of 50 registered voters in a particular city included 32 who favored using city funds for the construction of a new recreational facility. For this sample, pˆ= 32 = 0.64. If a 50 second random sample of 50 registered voters w
> The article referenced in the previous exercise also reported that 38% of the 1200 social network users surveyed said it was OK to ignore a coworker’s friend request. If pˆ = 0.38 is used as an estimate of the proportion of all social network users who b
> The article “facebook etiquette at work” (USA TODAY, march 24, 2010) reported that 56% of 1200 social network users surveyed indicated that they thought it was not OK for someone to “friend” his or her boss. Suppose that this sample can be regarded as a
> In a study of pet owners, it was reported that 24% celebrate their pet’s birthday (Pet Statistics, bissell homecare, inc., 2010). Suppose that this estimate was based on a random sample of 200 pet owners. Is it reasonable to conclude that the proportion
> Some colleges now allow students to rent textbooks for a semester. Suppose that 38% of all students enrolled at a particular college would rent textbooks if that option were available to them. If the campus bookstore uses a random sample of size 100 to e
> The report “a crisis in civic education” (january 2016, goacta.org/images/download/a_crisis_in_civic_education .pdf, retrieved may 3, 2017) indicated that in a survey of a random sample of 1000 recent college graduates, 96 indicated that they believed th
> The article “60% of employers are peeking into candidates’ Social media profiles” (careerbuilders, april 28, 2016, nscresearchcenter.org/wp-content/uploads/Snapshotreport17 -2Yearcontributions.pdf, retrieved october 9, 2016) included data from a survey o
> The article “cSi effect has juries wanting more evidence” (USA TODAY, august 5, 2004) examines how the popularity of crime-scene investigation television shows is influencing jurors’ expectations of w
> Suppose that 20% of the customers of a cable television company watch the Shopping Channel at least once a week. The cable company does not know the actual proportion of all customers who watch the Shopping Channel at least once a week and is trying to d
> The report “the role of two-Year institutions in fourYear Success” (national Student clearinghouse research center, 2015, nscresearchcenter.org/wp-content/uploads /Snapshotreport17-2Yearcontributions.pdf, retrieved may 3, 2017) states that nationwide, 46
> The article “Long-term effects of tongue piercing—a case-control Study” (Clinical Oral Investigations [2012]: 231– 237) describes a study of 46 males with pierced tongues. Suppose that it is reasonable to regard this sample as a random sample from the po
> The article “the average american is in credit card Debt, no matter the economy” (Money Magazine, february 9, 2016) reported that only 35% of credit card users pay off their bill every month. Suppose that the reported
> Suppose that a particular candidate for public office is favored by 48% of all registered voters in the district. A polling organization will take a random sample of 500 of these voters and will use pˆ, the sample proportion, to estimate p. a. Show that
> The article “facebook etiquette at work” (USA TODAY, March 24, 2010) reported that 56% of people participating in a survey of social network users said it was not OK for someone to “friend” his or her boss. Let p denote the proportion of all social netwo
> For which of the population proportions given in the previous exercise would the sampling distribution of pˆ be approximately normal if n = 40? If n = 75?
> A random sample of size 300 is to be selected from a population. Determine the mean and standard deviation of the sampling distribution of pˆ for each of the following population proportions. a. p = 0.20 b. p = 0.45 c. p = 0.70 d. p = 0.90
> For which of the following sample sizes would the sampling distribution of pˆ be approximately normal when p = 0.2? When p = 0.8? When p = 0.6? n = 10 n = 25 n = 50 n = 100
> Explain why the standard deviation of pˆ is equal to 0 when the population proportion is equal to 1.
> For which of the following combinations of sample size and population proportion would the standard deviation of pˆ be smallest? n = 40 p = 0.3 n = 60 p = 0.4 n = 100 p = 0.5
> The U.S. Census Bureau reported that in 2015 the proportion of adult Americans age 25 and older who have a bachelor’s degree or higher is 0.325 (“educational attainment in the United States: 2015,” www.census.gov, retrieved January 22, 2017). Consider th
> A certain chromosome defect occurs in only 1 in 200 adult Caucasian males. A random sample of 100 adult Caucasian males will be selected. The proportion of men in this sample who have the defect, pˆ, will be calculated. a. What are the mean and standard
> For which of the sample sizes given in the previous exercise would the sampling distribution of pˆ be approximately normal if p = 0.25? If p = 0.6?
> A random sample is to be selected from a population that has a proportion of successes p = 0.25. Determine the mean and standard deviation of the sampling distribution of pˆ for each of the following sample sizes: a. n = 10 b. n = 20 c. n = 30 d.
> The article referenced in the previous exercise also reported that for people age 18 to 29 who prefer to watch the news, the proportion that prefer to watch online is 0.37. Answer the questions posed in Parts (a)–(d) of the previous exercise for the popu
> The article “Younger adults more Likely than their elders to prefer reading the news” (October 6, 2016, www .pewresearch.org/fact-tank/2016/10/06/younger-adults -more-likely-than-their-elders-to-prefer-reading-news/) estimated that only 3% of those age 6
> For which of the sample sizes given in the previous exercise would the sampling distribution of p ˆ be approximately normal if p = 0.65? If p = 0.2?
> A random sample is to be selected from a population that has a proportion of successes p = 0.65. Determine the mean and standard deviation of the sampling distribution of pˆ for each of the following sample sizes: a. n = 10 b. n = 20 c. n = 30 d.
> Consider the following statement: A county tax assessor reported that the proportion of property owners who paid 2016 property taxes on time was 0.93. a. Is the number that appears in boldface in this statement a sample proportion or a population propor
> Consider the following statement: In a sample of 20 passengers selected from those who flew from Dallas to New York City in April 2017, the proportion who checked luggage was 0.45. a. Is the number that appears in boldface in this statement a sample pro
> Consider the two relative frequency histograms at the top of the next page. The histogram on the left was constructed by selecting 100 different random samples of size 35 from a population in which 17% donated to a nonprofit organization. For each sample
> Explain what it means when we say the value of a sample statistic varies from sample to sample.
> Consider the following statement: The proportion of all calls made to a county 9-1-1 emergency number during the year 2017 that were nonemergency calls was 0.14. a. Is the number that appears in boldface in this statement a sample proportion or a popula
> Consider the following statement: Fifty people were selected at random from those attending a football game. The proportion of these 50 who made a food or beverage purchase while at the game was 0.83. a. Is the number that appears in boldface in this st
> Explain what the term sampling variability means in the context of using a sample proportion to estimate a population proportion.
> Consider the two relative frequency histograms at the top of the next page. The histogram on the left was constructed by selecting 100 different random samples of size 40 from a population consisting of 20% part-time students and 80% full-time students.
> A random sample of 100 employees of a large company included 37 who had worked for the company for less than one year. For this sample, pˆ = 37 = 0.37. If a different 100 random sample of 100 employees were selected, would you expect that
> Explain the difference between p and pˆ.
> Consider the following statement: A sample of size 100 was selected from those admitted to a particular college in fall 2017. The proportion of these 100 who were transfer students is 0.38. a. Is the number that appears in boldface in this statement a s
> Consider the following statement: The Department of Motor Vehicles reports that the proportion of all vehicles registered in California that are imports is 0.22. a. Is the number that appears in boldface in this statement a sample proportion or a popula
> Consider the two relative frequency histograms at the bottom of this page. The histogram on the left was constructed by selecting 100 different random samples of size 50 from a population consisting of 55% females and 45% males. For each sample, the samp
> A random sample of 1000 students at a large college included 428 who had one or more credit cards. For this sample, pˆ = 428 = 0.428. If another random sample of 1000 students from 1000 this university were selected, would you expect
> The process for statistical inference described in Section 7.3 consists of five steps: a. What are the five steps in the process for estimation problems? b. Explain how the first step differs for estimation problems and hypothesis testing problems.
> The authors of the paper “flat-footedness is not a Disadvantage for athletic Performance in children aged 11 to 15 Years” (Pediatrics [2009]: e386–e392) collected data from 218 children on foot arch h
> In a study to determine if using low-intensity laser therapy reduces pain for orthodontic patients who are fitted with new braces, patients were randomly assigned to either a control group (who did not receive laser treatment) and an experimental group w
> Refer to the instructions prior to this exercise. A study of adult Americans conducted by the polling organization Ipsos (“One in Five Americans Consider Themselves ‘Entrepreneurs,’”
> Suppose that a study was carried out in which each student in a random sample of students at a particular college was asked if he or she was registered to vote. Would these data be used to estimate a population mean or to estimate a population proportion
> In a study of whether taking a garlic supplement reduces the risk of getting a cold, 146 participants were randomly assigned to either a garlic supplement group or to a group that did not take a garlic supplement (“Garlic for the Common Cold,” Cochrane D
> In the paper “happiness for Sale: Do experiential purchases make consumers happier than material purchases?” (Journal of Consumer Research [2009]: 188–197), the authors distinguish between spending mo
> If you deposit a $20 bill into a checking account and your bank has a 10 percent reserve requirement, by how much will the bank’s excess reserves rise?
> Briefly describe the effect on the money supply of the following monetary policies: a. The Fed purchases $20 million worth of U.S. Treasury bonds. b. The Fed increases the discount rate. c. The Fed decreases the discount rate. d. The Fed sells $40 millio
> Should the Fed be independent or a government agency subordinate to Congress and the president?
> Distinguish between M1 and M2. What are near monies?
> What backs the U.S. dollar? Include the distinction between commodity money and fiat money in your answer.
> Could each of the following items potentially serve as money? Consider each as a medium of exchange, a unit of account, or a store of value. a. Visa credit card. b. Federal Reserve note. c. Debit card. d. Picasso painting.
> Briefly discuss the importance of the Depository Institutions Deregulation and Monetary Control Act of 1980.
> Suppose the media report that the federal deficit this year is $200 billion. The national debt was $5,000 billion last year, and it is $5,200 billion this year. The price level this year is 3 percent higher than it was last year. What is the real deficit
> Explain the theory that crowding out can weaken or nullify the effect of expansionary fiscal policy financed by federal government borrowing.
> Explain this statement: “The most unlikely problem of the national debt is that the government will go bankrupt.”
> The following is a set of hypothetical production possibilities for a nation. a. Plot these production possibilities data. What is the opportunity cost of the first 2,000 automobiles produced? Between which points is the opportunity cost per thousand a
> Discuss various ways of measuring the size of the national debt.
> Consider this statement: “Our grandchildren may not suffer the entire burden of a federal deficit.” Do you agree or disagree? Explain.
> Explain why each of the following taxes is progressive or regressive. a. A $1 per pack federal excise tax on cigarettes. b. The federal individual income tax. c. The federal payroll tax.
> Explain why a 5 percent sales tax on gasoline is regressive.
> Which of the following taxes satisfy the benefits received principle, and which satisfy the ability to pay principle? a. Gasoline tax b. Federal income tax c. Tax on Social Security benefits
> What are the four largest categories of expenditures of the federal government?
> Calculate the average and marginal tax rates in the following table, and indicate whether the tax is progressive, proportional, or regressive. What observation can you make concerning the relationship between marginal and average tax rates? Average
> What is the difference between discretionary fiscal policy and automatic stabilizers? How are federal budget surpluses and deficits affected by the business cycle?
> Consider an economy that is operating at the full employment level of real GDP. Assuming the MPC is 0.90, predict the effect on the economy of a $50 billion increase in government spending balanced by a $50 billion increase in taxes.
> Why does a reduction in taxes have a smaller multiplier effect than an increase in government spending of an equal amount?
> Analyze the positive versus normative arguments in the following case. What statements of positive economics are used to support requiring air bags? What normative reasoning is used?
> How does each of the following affect the aggregate demand curve? a. Government spending increases. b. The amount of taxes collected decreases.
> Suppose Congress enacts a tax reform law and the average federal tax rate drops from 30 percent to 20 percent. Researchers investigate the impact of the tax cut and find that the income subject to the tax increases from $600 billion to $800 billion. The
> In the first quarter of 2001, real GDP was $9.88 trillion, and the price level measured by the GDP chain price index was 101. Real GDP was approximately equal to potential GDP. In the third quarter, aggregate demand decreased to $9.83 trillion, and the p
> Based on the assumptions of Question 3, explain verbally the impact of an increase of $4 trillion in aggregate demand on short-run equilibrium.
> Using the graph from Question 1 and assuming long run equilibrium at $12 trillion, explain the impact of a 10 percent increase in workers’ income.
> Assume an economy operates in the intermediate range of its aggregate supply curve. State the direction of shift for the aggregate demand or aggregate supply curve for each of the following changes in conditions. What is the effect on the price level? On
> Assume the aggregate demand and aggregate supply curves intersect at a price level of 100. Explain the effect of a shift in the price level to 120 and to 50.
> Identify the three ranges of the aggregate supply curve. Explain the impact of an increase in the aggregate demand curve in each segment.
> Explain the theory of the classical economists that flexible prices and wages ensure that the economy operates at full employment.
> Explain cost-push inflation verbally and graphically, using aggregate demand and aggregate supply analysis. Assess the impact on the price level, real GDP, and employment.
> Which of the following decisions has the greater opportunity cost? Why? a. A decision to use an undeveloped lot in Tokyo’s financial district for an apartment building. b. A decision to use a square mile in the desert for a gas station.
> Suppose the annual nominal rate of interest on a bank certificate of deposit is 12 percent. What would be the effect of an inflation rate of 13 percent?
> Who loses from inflation? Who wins from inflation?
> Suppose you earned $100,000 in a given year. Calculate your real income, assuming the CPI is 200 for this year.
> Suppose, in the base year, a typical market basket purchased by an urban family cost $250. In Year 1, the same market basket cost $950. What is the consumer price index (CPI) for Year 1? If the same market basket cost $1,000 in Year 2, what is the CPI fo
> How does demand-pull inflation differ from cost-push inflation?
> Explain why the market price may not be the same as the equilibrium price.
> Is it reasonable to expect the unemployment rate to fall to zero for an economy? What is the relationship of frictional, structural, and cyclical unemployment to the full-employment rate of unemployment, or natural rate of unemployment?
> Predict the direction of change for either supply or demand in the following situations: a. Several new companies enter the cell phone industry. b. Consumers suddenly decide SUVs are unfashionable. c. The U.S. surgeon general issues a report stating that
> Why is frictional unemployment inevitable in an economy characterized by imperfect job information?
> Draw graphs to illustrate the difference between a decrease in quantity supplied and a decrease in supply for condominiums. Give a possible reason for change in each graph.
> Explain the importance of the ceteris paribus assumption for an economic model.
> Describe the relevant criteria that government statisticians use to determine whether a person is “unemployed.”
> Draw graphs to illustrate the difference between a decrease in the quantity demanded and a decrease in demand for Mickey Mantle baseball cards. Give a possible reason for change in each graph.
> Following are real GDP figures for 10 quarters: Plot these data points, and identify the four phases of the business cycle. Give a theory that may explain the cause of the observed business cycle. What are some of the consequences of a prolonged declin
> Consider Exhibit 12, which shows the graph of a perfectly competitive firm in the short run. a. If the firm’s demand curve is MR3, does the firm earn an economic profit or loss? b. Which demand curve(s) indicate(s) the firm incurs a loss? c. Which demand
