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Essentials Of Business Statistics Communicating With Numbers 1st Edition Sanjiv Jaggia, Alison Kelly - Solutions

Consider the following hypotheses:H0: µ ≥ 150HA: µ < 150A sample of 80 observations results in a sample mean of 144.The population standard deviation is known to be 28.a. What is the critical value for the test with α = 0.01 and with α = 0.05?b. Does the above sample evidence enable us to
Redo the preceding question using the p-value approach.
Consider the following hypotheses:H0: µ = 1800HA: µ ≠ 1800The population is normally distributed with a population standard deviation of 440. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can reject
Consider the following hypotheses:H0: µ = 120HA: µ ≠ 120The population is normally distributed with a population standard deviation of 46.a. Use a 5% level of significance to determine the critical value(s) of the test.b. What is the conclusion with = 132 and n = 50?c. Use a 10% level of
Consider the following hypothesis test:H0: µ = -100HA: µ ≠ -100A random sample of 36 observations yields a sample mean of -125. The population standard deviation is 42. If α = 0.01, find the critical value(s). What is the conclusion to the test?
Customers at Costco spend an average of $130 per trip (The Wall Street Journal, October 6, 2010). One of Costco’s rivals would like to determine whether its customers spend more per trip. A survey of the receipts of 25 customers found that the sample mean was $135.25. Assume that the population
It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 36 small cars at 65 miles per hour and records the braking
An article in the National Geographic News (February 24, 2005) reports that Americans are increasingly skimping on their sleep. A researcher wants to determine if Americans are sleeping less than the recommended 7 hours of sleep on weekdays. He takes a random sample of 150 Americans and computes
In May 2008 CNN reported that sports utility vehicles (SUVs) are plunging toward the “endangered” list. Due to soaring oil prices and environmental concerns, consumers are replacing gas-guzzling vehicles with fuel-efficient smaller cars. As a result, there has been a big drop in the demand for
A local bottler in Hawaii wishes to ensure that an average of 16 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 48 bottles. The mean weight of the passion fruit juice in the sample is 15.80 ounces.
A Realtor in Mission Viejo, California, believes that the average price of a house is more than $500 thousand.a. State the null and the alternative hypotheses for the test.b. Open the MV_Houses data from the text website into an Excel spreadsheet (data are in $1,000s). Use the function Z.TEST to
Access the hourly wage data on the text website (Hourly_Wage). An economist wants to test if the average hourly wage is less than $22.a. State the null and the alternative hypotheses for the test.b. Use the function Z.TEST to calculate the p-value. Assume that the population standard deviation is
Access the weekly stock price data for Home Depot on the text website (Home_Depot). Assume that returns are normally distributed with a population standard deviation of $3.a. State the null and the alternative hypotheses in order to test whether or not the average weekly price differs from $30.b.
On average, a college student last year graduated with $27,200 in debt (The Boston Globe, May 27, 2012). A researcher collects data on debt from 40 recent undergraduates from Connecticut. The data set, labeled CT_Undergrad_Debt, can be found on the text website.Assume that the population standard
Consider the following hypotheses:H0: µ ≤ 210HA: µ > 210Approximate the p-value for this test based on the following sample information.a. = 216; s = 26; n = 40b. = 216; s = 26; n = 80c. = 216; s = 16; n = 40d. = 214; s = 16; n = 40
Which of the sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?
Consider the following hypotheses:H0: µ = 12HA: µ ≠ 12Approximate the p-value for this test based on the following sample information.a. = 11; s = 3.2; n = 36b. = 13; s = 3.2; n = 36c. = 11; s = 2.8; n = 36d. = 11; s = 2.8; n = 49
Which of the sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10? Discuss.
Determine the critical values for the following tests of the population mean with an unknown population standard deviation. The analysis is based on 18 observations drawn from a normally distributed population at a 1% level of significance.a. H0: µ ≤ 52 versus HA: µ > 52b. H0: µ = 9.2 versus
In order to conduct a hypothesis test of the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 4.8 and 0.8, respectively.Use the p-value approach to conduct the following tests at α =
Use the critical value approach to conduct the same two tests in the preceding question at α = 0.05.
In order to test if the population mean differs from 16, you draw a random sample of 32 observations and compute the sample mean and the sample standard deviation as 15.2 and 0.6, respectively. Use(a) The p-value approach and(b) The critical value approach to implement the test at a 1% level of
Consider the following hypotheses:H0: µ = 8HA: µ ≠ 8The population is normally distributed. A sample produces the following observations:Use the p-value approach to conduct the test at a 5% level ofsignificance.
Consider the following hypotheses:H0: µ ‰¥ 100HA: µ The population is normally distributed. A sample produces the following observations:Use the critical value approach to conduct the test at a 1% level ofsignificance.
A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively.a. Set up the null and the alternative hypotheses to determine if the machine is
The manager of a small convenience store does not want her customers standing in line for too long prior to a purchase. In particular, she is willing to hire an employee for another cash register if the average wait time of the customers is more than five minutes. She randomly observes the wait
Small, energy-efficient, Internet-centric, new computers are increasingly gaining popularity (New York Times, July 20, 2008). These computers, often called net-books, have scant onboard memory and are intended largely for surfing websites and checking e-mail. Some of the biggest companies are wary
A local brewery wishes to ensure that an average of 12 ounces of beer is used to fill each bottle. In order to analyze the accuracy of the bottling process, the bottler takes a random sample of 48 bottles. The sample mean weight and the sample standard deviation of the bottles are 11.80 ounces and
Based on the average predictions of 47 members of the National Association of Business Economists (NABE), the U.S. gross domestic product (GDP) will expand by 3.2% in 2011 (The Wall Street Journal, May 23, 2010). Suppose the sample standard deviation of their predictions was 1%. At a 5%
A car manufacturer is trying to develop a new sports car. Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The car company tested 12 of the cars and clocked their performance times. Three of the cars clocked in at 5.8
In September 2007, U.S. home prices continued to fall at a record pace, and price declines in Los Angeles and Orange counties in California outpaced other major metropolitan areas (Los Angeles Times, November 28, 2007). The report was based on the Standard & Poor’s/Case-Shiller index that
A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He studies the following sample APR quotes. These are the annual percentage rates (APR) for 30-year fixed loans. If he is willing to assume that these rates are randomly drawn from a normally distributed
One of the consequences of the economic meltdown has been a free fall of the stock market’s average price/earnings ratio, or P/E ratio (The Wall Street Journal, August 30, 2010). Generally, a high P/E ratio suggests that investors are expecting higher earnings growth in the future compared to
Access the miles per gallon data (MPG) on the text website.a. State the null and the alternative hypotheses in order to test whether the average MPG differs from 95.b. Use Excel to calculate the value of the test statistic and the exact p-value.c. At α = 0.05, can you conclude that the average MPG
A recent study found that consumers are making average monthly debt payments of $983 (Experian.com, November 11, 2010). The accompanying table shows a portion of average debt payments for 26 metropolitan areas. The complete data set, labeled Debt_Payments, can be found on the text website.CityDebt
A police officer is concerned about speeds on a certain section of Interstate 95. He records the speeds of 40 cars on a Saturday afternoon. The data set, labeled Highway_Speeds, can be found on the text website.a. The speed limit on this portion of Interstate 95 is 65 mph. Specify the competing
A recent article found that Massachusetts residents spent an average of $860.70 on the lottery in 2010, more than three times the U.S. average (www.businessweek.com, March 14, 2012). A researcher at a Boston think tank believes that Massachusetts residents spend significantly less than this amount.
Consider the following hypotheses:H0: p ≥ 0.38HA: p < 0.38Compute the p-value based on the following sample information.a. x = 22; n = 74b. x = 110; n = 300c. = 0.34; n = 50d. = 0.34; n = 400
Which sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?
Consider the following hypotheses:H0: p = 0.32HA: p ≠ 0.32Compute the p-value based on the following sample informationa. x = 20; n = 66b. x = 100; n = 264c. = 0.40; n = 40d. = 0.38; n = 180
Which sample information in the preceding question enables us to reject the null hypothesis at α = 0.05 and at α = 0.10?
Specify the critical value(s) for the following tests of the population proportion. The analysis is conducted at a 5% level of significance.a. H0: p ≤ 0.22; HA: p > 0.22b. H0: p = 0.69; HA: p ≠ 0.69c. H0: p ≥ 0.56; HA: p < 0.56
In order to conduct a hypothesis test of the population proportion, you sample 320 observations that result in 128 successes. Use the p-value approach to conduct the following tests at α = 0.05.a. H0: p ≥ 0.45; HA: p < 0.45b. H0: p = 0.45; HA: p ≠ 0.45
Repeat the preceding exercise using the critical value approach at α = 0.01.
You would like to determine if the population probability of success differs from 0.70. You find 62 successes in 80 binomial trials. Implement the test at a 1% level of significance.
You would like to determine if more than 50% of the observations in a population are below 10. At Î± = 0.05, conduct the test on the basis of the following 20 sampleobservations:
A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether
Due to the recent economic downturn, Americans have started raiding their already fragile retirement accounts to endure financial hardships such as unemployment, medical emergencies, and buying a home (MSN Money, July 16, 2008). It is reported that between 1998 and 2004, about 12% of families with
The margarita is one of the most common tequila-based cocktails, made with tequila mixed with Triple Sec and lime or lemon juice, often served with salt on the glass rim.A common ratio for a margarita is 2:1:1, which includes 50% tequila, 25% Triple Sec, and 25% fresh lime or lemon juice. A manager
A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a second time. Their target is to have 30 million viewers, and they want more than 30% of the viewers to return to see the movie again. They show the movie to a test audience
Recent research commissioned by Vodafone suggests that older workers are the happiest employees (BBC News, July 21, 2008). The report documents that 70% of older workers in England feel fulfilled, compared with just 50% of younger workers. A demographer believes that an identical pattern does not
A politician claims that he is supported by a clear majority of voters. In a recent survey, 24 out of 40 randomly selected voters indicated that they would vote for the politician. Is the politician’s claim justifiable at a 5% level of significance?
New research shows that many banks are unwittingly training their online customers to take risks with their passwords and other sensitive account information, leaving them more vulnerable to fraud (Yahoo.com, July 23, 2008).Even web-savvy surfers could find themselves the victims of identity theft
The Social Security Administration is not expected to provide any increases in Social Security benefits for the second straight year (US News & World Report, October 4, 2010).With increasing medical prices, it is claimed that more than 60% of seniors are likely to make serious adjustments to their
According to a report on workforce diversity, about 60% of the employees in high-tech firms in Silicon Valley are whites and about 20% are Asians (moneycnn.com, November 9, 2011). Women, along with blacks and Hispanics, are highly underrepresented.Just about 30% of all employees are women, with
A pharmaceutical company has developed a new drug for depression. There is a concern, however, that the drug also raises the blood pressure of its users. A researcher wants to conduct a test to validate this claim. Is the manager of the pharmaceutical company more concerned about Type I or Type II
A company has developed a new diet that it claims will lower one’s weight by more than 10 pounds. Health officials decide to conduct a test to validate this claim.a. Is the manager of the company more concerned about Type I or Type II error? Explain.b. Should the consumers be more concerned about
A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life of just 5 hours. The manufacturer claims that while the new touch phone is more expensive, its battery life is more than twice as long as that of the leading product. In
An advertisement for a popular weight loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight reduction program. She
A city council is deciding whether or not to spend additional money to reduce the amount of traffic. The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 20 minutes. A sample of 32 main roads results in a mean waiting time of 22.08
Rates on 30-year fixed mortgages continue to be at historic lows (Chron Business News, September 23, 2010).According to Freddie Mac, the average rate for 30-year fixed loans for the week was 4.37%. An economist wants to test if there is any change in the mortgage rates in the following week. She
Using data from the past 25 years, an investor wants to test whether the average return of Vanguard’s Precious Metals and Mining Fund is greater than 12%. Assume returns are normally distributed with a population standard deviation of 30%.a. State the null and the alternative hypotheses for the
An entrepreneur examines monthly sales (in $1,000s) for 40 convenience stores in Rhode Island. Access the convenience store sales data on the text website (Convenience_Stores).a. State the null and the alternative hypotheses in order to test whether average sales differ from $130,000.b. Use Excel
On average, Americans drive 13,500 miles per year (The Boston Globe, June 7, 2012). An economist gathers data on the driving habits of 50 residents in the Midwest. The data set, labeled Midwest_Drivers, can be found on the text website.a. The economist believes that the average number of miles
The euro-zone crisis continues to wreak havoc on U.S. stock markets (The Wall Street Journal, June 8, 2012). A portfolio analyst wonders if the average trading volume on the Dow Jones Industrial Average (DJIA) has increased since the beginning of the year. She gathers data on daily trading
A retailer is looking to evaluate its customer service. Management has determined that if the retailer wants to stay competitive, then it will have to have at least a 90% satisfaction rate among its customers. Management will take corrective actions if the satisfaction rate falls below 90%. A
The lingering economic crisis has cost America trillions of dollars in lost wealth and also has levied a heavy toll on the national psyche (The Wall Street Journal, December 21, 2009).According to a recent poll, just 33% of those surveyed said America was headed in the right direction. Suppose this
A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch.
A Pew Research study finds that 23% of Americans use only a cell phone, and no land line, for making phone calls (The Wall Street Journal, October 14, 2010). A year later, a researcher samples 200 Americans and finds that 51 of them use only cell phones for making phone calls.a. Set up the
A national survey found that 33% of high school students said they texted or e-mailed while driving (The Boston Globe, June 8, 2012). These findings came a day after a Massachusetts teenager was convicted for causing a fatal crash while texting. A researcher wonders whether texting or e-mailing
A recent report suggests that business majors spend the least amount of time on course work than do all other college students (New York Times, November 17, 2011). A provost of a university conducts a survey of 50 business and 50 non-business students. Students are asked if they study hard, defined
Construct the null and the alternative hypotheses for the following tests:a. Test if the mean weight of cereal in a cereal box differs from 18 ounces.b. Test if the stock price increases on more than 60% of the trading days.c. Test if Americans get an average of less than seven hours of sleep.
Construct the null and the alternative hypotheses for the following claims:a. “I am going to get the majority of the votes to win this election.”b. “I suspect that your 10-inch pizzas are, on average, less than 10 inches in size.”c. “I will have to fine the company since its tablets do
Consider the following hypothesis test:H0: µ ≤ -5HA: µ > -25A random sample of 25 observations yields a sample mean of 28. The population standard deviation is 10. Calculate the p-value. What is the conclusion to the test if α = 0.05?
Consider the following hypothesis test:H0: µ ≥ 75HA: µ < 75A random sample of 100 observations yields a sample mean of 80. The population standard deviation is 30. Calculate the p-value. What is the conclusion to the test if α = 0.10?
Harvard University has recently revolutionized its financial aid policies, aimed at easing the financial strain on middle and upper-middle income families (Newsweek, August 18â€“25, 2008). The expected contribution of students who are admitted to Harvard has been greatly reduced. Many other
The effort to reward city students for passing Advanced Placement tests is part of a growing trend nationally and internationally. Financial incentives are offered in order to lift attendance and achievement rates. One such program in Dallas, Texas, offers $100 for every Advanced Placement test on
The Gallup-Healthways Well-Being Index (www.well-beingindex.com) provides an assessment measure of health and well-being of U.S. residents. By collecting periodic data on life evaluation, physical health, emotional health, healthy behavior, work environment, and basic access, this assessment
In a simple linear regression, the following information is given:= 34; = 44; ((xi - )(yi â€“ ) = 1250;((xi - )2 = 925a. Calculate b1.b. Calculate b0.c. What is the sample regression equation? Predict y if x equals 40.
In a simple linear regression, the following information is given:= -25; = 56; Σ (xi -) (yi -) = -866 ; Σ(xi -)2 = 711a. Calculate b1.b. Calculate b0.c. What is the sample regression equation? Predict y if x equals −20.
In a simple linear regression, the following sample regression equation is obtained:y̅= 15 + 2.5x.a. Predict y if x equals 10.b. What happens to this prediction if x doubles in value?
In a simple linear regression, the following sample regression equation is obtained:y̅ = 436 - 17x.a. Interpret the slope coefficient.b. Predict y if x equals −15.
Consider the following sample data:a. Construct a scatter plot and verify that estimating a simple linear regression model is appropriate in this problem.b. Calculate b1 and b0. What is the sample regression equation?c. Find the predicted value for y if x equals 10, 15, and20.
Consider the following sample data:a. Construct a scatter plot and verify that estimating a simple linear regression model is appropriate in this problem.b. Calculate b0 and b1. What is the sample regression equation?c. Find the predicted value for y if x equals 15, 20, and25.
Thirty observations were used to estimate y = Î²0 + Î² 1x + .A portion of the Excel results is as follows:a. What is the point estimate for Î²1? Interpret this value.b. What is the sample regression equation?c. If x = 30, what isy?
Twenty-four observations were used to estimate y = Î²0 + Î²1x + . A portion of the Excel results is as follows:a. What is the point estimate for Î²1? Interpret this value.b. What is the sample regression equation?c. What is the predicted value for y if x = 2? If x =-2?
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 studentâ€™s grade point average (GPA). She uses a sample of 8
A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individualâ€™s annual salary in thousands of dollars:a. Find the sample regression
The owner of several used-car dealerships believes that the selling price of a used car can best be predicted using the carâ€™s age. He uses data on the recent selling price and age of 20 used sedans to estimate Price = Î²0 + Î²1Age + .AÂ portion of the Excel results is as follows:a.
If a firm spends more on advertising, is it likely to increase sales? Data on annual sales (in $100,000s) and advertising expenditures (in $10,000s) were collected for 20 firms in order to estimate the model Sales = Î²0 + Î²1 Advertising + .A portion of the Excel results is as follows:a. Is the
The consumption function captures one of the key relationships in economics that was first developed by JohnÂ Maynard Keynes. It expresses consumption as a function of disposable income, where disposable income is income after taxes. The table below shows a portion of average U.S. annual
The following table lists Major League Baseballâ€™s (MLBâ€™s) leading pitchers, their earned run average (ERA), and their salary (in millions of dollars) for 2008. The entire data set, labeled MLB_Pitchers, can be found on the text website.a. Use Excel to estimate the model: Salary =
In order to answer the following questions, use the data labeled Happiness_Age on the text website.a. Use Excel to estimate a simple linear regression model with Happiness as the response variable and Age as the explanatory variable.b. Use the estimates to predict Happiness when Age equals 25, 50,
The accompanying table shows a portion of the grades that 32 students obtained on the midterm and the final examinations in a course in statistics. The entire data set, labeled Test_Scores, can be found on the text website.MidtermFinal78.........8697.........94...........47.........91a. Determine
The accompanying table shows a portion of a data set that refers to the size of a home (in square feet) and its property taxes owed by the owner (in $) in an al fluent suburb 30 miles outside New York City. The entire data set, labeled Property_Taxes, can be found on the text website.a. Determine
In a multiple regression, the following sample regression equation is obtained: = 152 + 12.9x1 + 2.7x2.a. Predict y if x1 equals 20 and x2 equals 35.b. Interpret the slope coefficient of x1.
In a multiple regression, the following sample regression equation is obtained:y̅ = -8 + 2.6x1 - 47.2x2.a. Predict y if x1 equals 40 and x2 equals −10.b. Interpret the slope coefficient of x2.
Thirty observations were used to estimate y = β0 + β 1x1 + β 2x2 + ε. A portion of the Excel results is as follows:a. What is the point estimate for β1? Interpret this value.b. What is the sample regression equation?c. If x1 = 30 and x2 = 20, what is y̅?
Forty observations were used to estimate y = β0 + β1x1 + β2x2 + ε. A portion of the regression results is shown in the following table.a. What is the point estimate for β1? Interpret this value.b. What is the sample regression equation?c. What is the predicted value for y if x1 = 29 and x2 =25.
On the first day of class, an economics professor administers a test to gauge the math preparedness of her students. She believes that the performance on this math test and the number of hours studied per week on the course are the primary factors that predict a studentâ€™s score on the final

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