For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). He finds that SSE = 4,182,663 and SST = 7,732,451. a. Calculate the standard error of the estimate. b. What proportion of the sample variation in crime rate is explained by the variability in the explanatory variables? What proportion is unexplained?
> A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 90%. If it is known that returns are normally distributed with a mean of 5.6%, what is the risk, measured by standard deviation,
> Scores on a marketing exam are known to be normally distributed with a mean and a standard deviation of 60 and 20, respectively. a. Find the probability that a randomly selected student scores between 50 and 80. b. Find the probability that a randomly se
> An estimated 1.8 million students take on student loans to pay ever-rising tuition and room and board (The New York Times, April 17, 2009). It is also known that the average cumulative debt of recent college graduates is about $22,500. Let the cumulative
> The manager of a night club in Boston stated that 95% of the customers are between the ages of 22 and 28 years. If the age of customers is normally distributed with a mean of 25 years, calculate its standard deviation.
> Due to a crisis in subprime lending, obtaining a mortgage has become difficult even for people with solid credit. In a report by the Associated Press (August 25, 2007), sales of existing homes fell for a 5th consecutive month, while home prices dropped f
> A packaging system fills boxes to an average weight of 18 ounces with a standard deviation of 0.2 ounce. It is reasonable to assume that the weights are normally distributed. Calculate the 1st, 2nd, and 3rd quartiles of the box weight.
> A financial advisor informs a client that the expected return on a portfolio is 8% with a standard deviation of 12%. There is a 15% chance that the return would be above 16%. If the advisor is right about her assessment, is it reasonable to assume that t
> For a continuous random variable X, P (20 ≤ X ≤ 40) = 0.15 and P (X > 40) = 0.16. Calculate the following probabilities. a. P (X < 40) b. P (X < 20) c. P (X = 40)
> Let X be normally distributed with μ = −15 and σ = 9. a. Find P (X > −12). b. Find P (0 ≤ X ≤ 5). c. Find x such that P (X ≤ x) = 0.25. d. Find x such that P (X > x) = 0.25.
> Let X be normally distributed with μ = 254 and σ = 11. a. Find P (X ≤ 266). b. Find P (250 < X < 270). c. Find x such that P (X ≤ x) = 0.33. d. Find x such that P (X > x) = 0.33.
> The random variable X is normally distributed. Also, it is known that P (X > 150) = 0.10. a. Find the population mean μ if the population standard deviation σ = 15. b. Find the population mean μ if the population standard deviation σ = 25. c. Find the po
> Let X be normally distributed with mean μ = 2,500 and standard deviation σ = 800. a. Find x such that P (X ≤ x) = 0.9382. b. Find x such that P (X > x) = 0.025. c. Find x such that P (2500 ≤ X ≤ x) = 0.1217. d. Find x such that P (X ≤ x) = 0.4840.
> Find the following z values for the standard normal variable Z. a. P (Z ≤ z) = 0.1020 b. P (z ≤ Z ≤ 0) = 0.1772 c. P (Z > z) = 0.9929 d. P (0.40 ≤ Z ≤ z) = 0.3368
> Find the following z values for the standard normal variable Z. a. P (Z ≤ z) = 0.9744 b. P (Z > z) = 0.8389 c. P (−z ≤ Z ≤ z) = 0.95 d. P (0 ≤ Z ≤ z) = 0.3315
> Find the following probabilities based on the standard normal variable Z. a. P(−0.67 ≤ Z ≤ −0.23) b. P (0 ≤ Z ≤ 1.96) c. P (−1.28 ≤ Z ≤ 0) d. P (Z > 4.2)
> A study reports that recent college graduates from New Hampshire face the highest average debt of $31,048 (The Boston Globe, May 27, 2012). A researcher from Connecticut wants to determine how recent undergraduates from that state fare. He collects data
> Find the following probabilities based on the standard normal variable Z. a. P (Z > 0.74) b. P (Z ≤ −1.92) c. P (0 ≤ Z ≤ 1.62) d. P (−0.90 ≤ Z ≤ 2.94)
> Find the following probabilities based on the standard normal variable Z. a. P (Z > 1.32) b. P (Z ≤ −1.32) c. P (1.32 ≤ Z ≤ 2.37) d. P (−1.32 ≤ Z ≤ 2.37)
> You have been informed that the assessor will visit your home sometime between 10:00 am and 12:00 pm. It is reasonable to assume that his visitation time is uniformly distributed over the specified two-hour interval. Suppose you have to run a quick erran
> The scheduled arrival time for a daily flight from Boston to New York is 9:25 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:15 am and a late arrival time of 9:55 am. a. Calculat
> Forty-four percent of consumers with credit cards carry balances from month to month (bankrate.com, February 20, 2007). Four consumers with credit cards are randomly selected. a. What is the probability that all four consumers carry a credit card balance
> Fifty percent of the customers who go to Sears Auto Center for tires buy four tires and 30% buy two tires. Moreover, 18% buy fewer than two tires, with 5% buying none. a. Find the expected value and the standard deviation of the number of tires a custome
> Assume that X is a hypergeometric random variable with N = 25, S = 3, and n = 4. Calculate the following probabilities. a. P (X = 0) b. P (X = 1) c. P (X ≤ 1)
> Airline travelers should be ready to be more flexible as airlines once again cancel thousands of flights this summer. The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines (
> Motorists arrive at a Gulf gas station at the rate of two per minute during morning hours. a. What is the probability that more than two motorists will arrive at the Gulf gas station during a one-minute interval in the morning? b. What is the probability
> A textile manufacturing process finds that on average, two flaws occur per every 50 yards of material produced. a. What is the probability of exactly two flaws in a 50-yard piece of material? b. What is the probability of no more than two flaws in a 50-y
> An article in the National Geographic News (“U.S. Racking Up Huge Sleep Debt,” February 24, 2005) argues that Americans are increasingly skimping on their sleep. A researcher in a small Midwestern town wants to estimate the mean weekday sleep time of its
> A tollbooth operator has observed that cars arrive randomly at an average rate of 360 cars per hour. a. Find the probability that two cars arrive during a specified one-minute period. b. Find the probability that at least two cars arrive during a specifi
> Let the mean success rate of a Poisson process be 8 successes per hour. a. Find the expected number of successes in a half-hour period. b. Find the probability of at least two successes in a given half-hour period. c. Find the expected number of successe
> Assume that X is a Poisson random variable with μ = 4. Calculate the following probabilities. a. P (X = 4) b. P (X = 2) c. P (X ≤ 1)
> Assume that X is a Poisson random variable with μ = 1.5. Calculate the following probabilities. a. P (X = 1) b. P (X = 2) c. P (X ≥ 2)
> The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure during the one-year period ending in February 2008 (The Washington Post, June 19, 2008). Over the past year, the number of fo
> The principal of an architecture firm tells her client that there is at least a 50% chance of having an acceptable design by the end of the week. She knows that there is only a 25% chance that any one designer would be able to do so by the end of the wee
> Sixty percent of a firm’s employees are men. Suppose four of the firm’s employees are randomly selected. a. What is more likely, finding three men and one woman or two men and two women? b. Do you obtain the same answer as in part a if 70% of the firm’s
> According to the U.S. Census, roughly half of all marriages in the United States end in divorce. Researchers from leading universities have shown that the emotions aroused by one person’s divorce can transfer like a virus, making divorce contagious (CNN,
> Sikhism, a religion founded in the 15th century in India, is going through turmoil due to a rapid decline in the number of Sikh youths who wear turbans (The Washington Post, March 29, 2009). The tedious task of combing and tying up long hair and a desire
> In an analysis of Census figures, one in four American counties has passed or is approaching the tipping point where black, Hispanic, and Asian children constitute a majority of the under-20 population (The New York Times, August 6, 2008). Racial and eth
> In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 28 recent loans is taken. The average calculated from this sample is 5.25%. It can be assumed that 30-year fixed mortgage rates are normall
> Approximately 45% of Baby Boomers—those born between 1946 and 1964—are still in the workforce (www.pewresearch.org, May 11, 2015). Six Baby Boomers are selected at random. a. What is the probability that exactly one of the Baby Boomers is still in the wo
> According to a survey by Transamerica Center for Health Studies, 15% of Americans still have no health insurance even after passage of the Affordable Care Act, better known as Obamacare (www.cbsnews.com, September 24, 2014). Suppose five individuals are
> Let the probability of success on a Bernoulli trial be 0.30. In five Bernoulli trials, what is the probability that there will be (a) four failures, and (b) more than the expected number of failures?
> Assume that X is a binomial random variable with n = 8 and p = 0.32. Calculate the following probabilities. a. P (3 < X < 5) b. P (3 < X ≤ 5) c. P (3 ≤ X ≤ 5)
> Megan Hanson, a realtor in Brownsburg, Indiana, would like to use estimates from a multiple regression model to help prospective sellers determine a reasonable asking price for their homes. She believes that the following four factors influence the askin
> Akiko Hamaguchi, the manager at a small sushi restaurant in Phoenix, Arizona, is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. Her cousin in San Francisco, Hiroshi Sato, owns
> A local university offers its employees the following Fidelity investment products for their retirement plans: Fidelity Total Bond Fund Fidelity Short-Term Bond Fund Fidelity Magellan Fund Fidelity International Small Cap Fund Fidelity Freedom Income
> Executive compensation has risen dramatically beyond the rising levels of an average worker’s wage over the years. The government is even considering a cap on high-flying salaries for executives (The New York Times, February 9, 2009). C
> Assume that X is a binomial random variable with n = 6 and p = 0.68. Calculate the following probabilities. a. P (X = 5) b. P (X = 4) c. P (X ≥ 4)
> In a multiple regression with four explanatory variables and 100 observations, it is found that SSR = 4.75 and SST = 7.62. a. Calculate the standard error of the estimate se. b. Calculate the coefficient of determination R2. c. Calculate adjusted R2.
> A financial analyst uses the following model to estimate a firm’s stock return: Return = β0 + β1P⁄E + β2P/S + ε, where P/E is a firm’s price-to-earnings ratio and P/S is a firm’s price-to sales ratio. For a sample of 30 firms, she finds that SSE = 4,402.
> In a multiple regression with two explanatory variables, and 50 observations, it is found that SSE = 35 and SST = 90. a. Calculate the standard error of the estimate se. b. Calculate the coefficient of determination R2.
> The accompanying data file shows the midterm and final scores for 32 students in a statistics course. a. Estimate a student’s final score as a function of his/her midterm score. b. Find the standard error of the estimate. c. Find and interpret the coe
> In an attempt to determine whether or not a linear relationship exists between the price of a home (in $1,000s) and the number of days it takes to sell the home, a real estate agent collected data from recent sales in his city and estimated the following
> An engineer wants to determine whether the average strength of plywood boards (in pounds per square inch, psi) differs depending on the type of glue used. For three types of glue, she measures the strength of 20 plywood boards. A portion of the data is s
> A capital asset pricing model (CAPM) for Johnson & Johnson (J&J) was discussed in Example 15.3. The model uses the risk-adjusted stock return R − Rf for J&J as the response variable and the risk-adjusted market return RM − Rf as the explanatory variable.
> You have $400,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $200,000. Consider the summary measures in the following table: The correlation coefficient between your portfolio and the house is 0.38. a. What is
> The manager of an SAT review program wonders whether average SAT scores differ depending on the ethnicity of the test taker. Thirty test scores for four ethnicities are collected. A portion of the data is shown in the accompanying table. At the 5% sign
> An analyst estimates the sales of a firm as a function of its advertising expenditures using the model: Sales = β0 + β1Advertising + ε. Using 20 observations, he finds that SSR = 199.93 and SST = 240.92. a. What proportion of the sample variation in sal
> Consider the data on salary (in $) and work experience (in years) of 100 employees in a marketing firm. Estimate the model: Salary = β0 + β1Experience + ε. a. Explain why you would be concerned about changing variability in this application. b. Use a r
> The accompanying table lists goodness-of-fit measures that were obtained when estimating the following multiple linear regression models: Which model provides a better fit for y? Justify your response with two goodness-of-fit measures. Model 1: y=
> Consider the results of a survey where students were asked about their GPA and also to break down their typical 24-hour day into study, leisure (including work), and sleep. Consider the model GPA = β0 + β1Study + β2Leisure + β3Sleep + ε. a. What is wrong
> The accompanying table lists goodness-of-fit measures that were obtained when estimating the following simple linear regression model and multiple linear regression model: Which model provides a better fit for y? Justify your response with two goodnes
> Numerous studies have shown that watching too much television hurts school grades. Others have argued that television is not necessarily a bad thing for children (Mail Online, July 18, 2009). Like books and stories, television not only entertains, it als
> The accompanying table lists goodness-of-fit measures that were obtained when estimating the following simple linear regression model and multiple linear regression model: Which model provides a better fit for y? Justify your response with two goodnes
> Consider the following competing hypotheses and accompanying sample data. a. Calculate the value of the test statistic. b. Find the p-value. c. At the 5% significance level, what is the conclusion to the test? Can you conclude that the difference betwe
> Consider the following competing hypotheses and accompanying sample data. a. Calculate the value of the test statistic. b. Find the p-value. c. At the 5% significance level, what is the conclusion to the test? Do the population proportions differ?
> A pension fund manager is considering three mutual funds for investment. The first one is a stock fund, the second is a bond fund, and the third is a money market fund. The money market fund yields a risk-free return of 4%. The inputs for the risky funds
> Consider the following competing hypotheses and accompanying sample data. a. Calculate the value of the test statistic. b. Find the p-value. c. At the 5% significance level, what is the conclusion to the test? Do the population proportions differ?
> Consider the following competing hypotheses and accompanying sample data. a. Calculate the value of the test statistic. b. Find the p-value. c. At the 5% significance level, what is the conclusion to the test? Is p1 less than p2? Ho: Pi – P2 2 0 Hạ
> Given x1 = 50, n1 = 200, x2 = 70, n2 = 250, construct the 95% confidence interval for the difference between the population proportions. Is there a difference between the population proportions at the 5% significance level? Explain.
> Consider the following sample data drawn independently from normally distributed populations with unequal population variances. Sample 1 ……………………………………………………………………………………… Sample 2 88 …………………………………………………………………………………………………………. 98 110 ………………………………………………………
> The covariance between two random variables x and y is −250. The sample standard deviation for x is 40 and the sample standard deviation for y is 50. Calculate and interpret the correlation coefficient.
> The following table lists a portion of Major League Baseball’s (MLB’s) leading pitchers, each pitcher’s salary (In $ millions), and earned run average (ERA) for 2008. a. Estimate the model: Salary =
> The consumption function, first developed by John Maynard Keynes, captures one of the key relationships in economics. It expresses consumption as a function of disposable income, where disposable income is income after taxes. The accompanying table shows
> The director of graduate admissions at a large university is analyzing the relationship between scores on the math portion of the Graduate Record Examination (GRE) and subsequent performance in graduate school, as measured by a student’s grade point aver
> The accompanying table shows a portion of the scores that 32 students obtained on the final and the midterm in a course in statistics. Final …………………………………………………………………………………………………… Midterm 86 ………………………………………………………………………………………………………………… 78 94 ………………………………
> The accompanying table shows a portion of the average price of gas (in $ per gallon) for the 50 states during April 2012. State ………………………………………………………………………………………………… Price Alabama ……………………………………………………………………………………………….. 4.36 Alaska …………………………………………………………
> The accompanying table shows a portion of data that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City. Property …………………………………………………………………………………………... Ta
> Construct the 90% interval estimate for the ratio of the population variances using the following results from two independently drawn samples from normally distributed populations. Sample 1: x1 = 157, s = 23.2, and n = 9 Sample 2: x2 = 148, s = 19.
> Use the F table to find the following probabilities. F table: a. P (F (10,8) ≥ 3.35) b. P (F (10,8) c. P (F (10,8) ≥ 4.30) d. P (F (10,8) dfi df2 Area in Upper Tail, a 6 7 8 0.10 3.05 3.01 2.98 0.05 4.28 4.21 4.15
> Consider the following competing hypotheses and accompanying results from a matched pairs sample: a. Calculate the value of the test statistic and the p-value, assuming that the sample difference is normally distributed. b. Use the 1% significance leve
> Consider the following competing hypotheses and accompanying results from a matched pairs sample: a. Calculate the value of the test statistic and the p-value, assuming that the sample difference is normally distributed. b. At the 5% significance level
> The following table contains information on matched sample values whose differences are normally distributed. a. Construct the 95% confidence interval for the mean difference μD. b. Specify the competing hypotheses in order to test whethe
> In a simple linear regression, the following sample regression equation is obtained: a. Predict y if x equals 10. b. What happens to this prediction if x doubles in value to 20? ŷ = 15 + 2.5x.
> The accompanying table shows a portion of the number of cases of crime related to gambling (Gambling) and offenses against the family and children (Family Abuse) for the 50 states in the United States during 2010. a. Construct a boxplot for gambling an
> Go to the U.S. Census Bureau website at www.census.gov/ and extract the most recent median household income for Alabama, Arizona, California, Florida, Georgia, Indiana, Iowa, Maine, Massachusetts, Minnesota, Mississippi, New Mexico, North Dakota, and Was
> An article in The Wall Street Journal (July 11, 2008) outlined a number of reasons as to why the 16 teams in Major League Baseball’s National League (NL) are inferior to the 14 teams in the American League (AL). One reason for the imbal
> The French Bread Company also allocates fixed manufacturing overhead to products on the basis of standard direct manufacturing labor-hours. For 2012, fixed manufacturing overhead was budgeted at $4.00 per direct manufacturing labor-hour. Actual fixed m
> The French Bread Company bakes baguettes for distribution to upscale grocery stores. The company has two direct-cost categories: direct materials and direct manufacturing labor. Variable manufacturing overhead is allocated to products on the basis of sta
> Esquire Clothing allocates fixed manufacturing overhead to each suit using budgeted direct manufacturing labor-hours per suit. Data pertaining to fixed manufacturing overhead costs for June 2012 are budgeted, $62,400, and actual, $63,916. Required: 1. C
> Esquire Clothing is a manufacturer of designer suits. The cost of each suit is the sum of three variable costs (direct material costs, direct manufacturing labor costs, and manufacturing overhead costs) and one fixed-cost category (manufacturing overhead
> Rhaden Company produces sweat-resistant headbands for joggers. Information pertaining to Rhaden’s operations for May 2011 follows: Required: 1. Compute the sales volume variance for May 2011. 2. Compute the market-share and market-siz
> Suppose the static budget was for 2,500 units of output. Actual output was 2,000 units. The variances are shown in the following report: Required: What are the price, efficiency, and sales-volume variances for direct materials and direct manufacturing
> Prepare journal entries and post them to T-accounts for all transactions in Exercise 7-26, including requirement 2. Summarize how these journal entries differ from the normal-costing entries described in Chapter 4, pages 112–114. Data
> Dunn, Inc., is a privately held furniture manufacturer. For August 2012, Dunn had the following standards for one of its products, a wicker chair: The following data were compiled regarding actual performance : actual output units (chairs) produced, 2,
> The Monroe Corporation sets monthly standard costs using a continuous-improvement approach. In January 2012, the standard direct material cost is $45 per unit and the standard direct manufacturing labor cost is $15 per unit. Due to more efficient operati
> The Monroe Corporation manufactures lamps. It has set up the following standards per finished unit for direct materials and direct manufacturing labor: The number of finished units budgeted for January 2012 was 10,000; 9,850 units were actually produce
> Budgets meet the cost-benefit test. They force managers to act differently.” Do you agree? Explain.
> GloriaDee, Inc., designs and manufactures T-shirts. It sells its T-shirts to brand-name clothes retailers in lots of one dozen. GloriaDee’s May 2011 static budget and actual results for direct inputs are as follows: GloriaDee has a po
> .Peterson Foods manufactures pumpkin scones. For January 2012, it budgeted to purchase and use 15,000 pounds of pumpkin at $0.89 a pound. Actual purchases and usage for January 2012 were 16,000 pounds at $0.82 a pound. Peterson budgeted for 60,000 pumpki
> Marron, Inc., produces the basic fillings used in many popular frozen desserts and treats—vanilla and chocolate ice creams, puddings, meringues, and fudge. Marron uses standard costing and carries over no inventory from one month to the
