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business statistics communicating

Business Statistics Communicating With Numbers 3rd Edition Sanjiv Jaggia - Solutions

The accompanying data file shows the annual return (in percent) for the Fidelity Select Technology Fund and the Fidelity Select Energy Fund from 2000 through 2016. Assume that the return data are bell-shaped.a. Use z-scores to determine if there are any outliers in the technology return data.b. Use
An environmentalist wants to examine whether average fuel consumption (measured in miles per gallon) is affected by fuel type (factor A) and type of hybrid (factor B). A two-way ANOVA experiment with interaction is performed. The results are shown in the accompanying table.a. At the 5% significance
A data analyst for an online store wonders whether average customer visits to the store’s website vary by day of the week. He collects daily unique visits to the website for a 12-week period; a portion of the data is shown in the accompanying table. At the 5% significance level, what conclusion
The following observations were obtained when conducting a two-way ANOVA experiment with no interaction.a. Calculate SST, SSA, SSB, and SSE.b. Calculate MSA, MSB, and MSE.c. Construct an ANOVA table.d. At the 5% significance level, can you conclude that the column means differ?e. At the 5%
A one-way analysis of variance experiment produced the following ANOVA table.a. Use Fisher’s LSD method to determine which means differ at the 5% level of significance.b. Use Tukey’s HSD method to determine which means differ at the 5% level of significance.c. Given your responses to parts (a)
The value of a college degree is greater than it has been in nearly half a century, at least when compared to the prospect of not getting a degree (www.pewresearch.org, January 28, 2014). Due to this fact, more and more people are obtaining college degrees, despite the soaring costs. The
Despite Zimbabwe’s shattered economy, with endemic poverty and widespread political strife and repression, thousands of people from overseas still head there every year (BBC News, August 27, 2008). Main attractions include the magnificent Victoria Falls, the ruins of Great Zimbabwe, and herds of
In a report, use the below information to 1. Describe the similarities and differences in these two funds’ returns.2. Examine whether the risk of one fund is different from the risk of the other fund at the 5% significance level. Discuss the assumptions made for the analysis.Nicholas Grammas
Adidas revenues (in millions of €) in the Greater China and Western Europe regions for the years 2011 through 2015 are shown in the accompanying table. Assume revenues are normally distributed.a. Specify the competing hypotheses in order to test whether the variance in revenues is greater in the
Barbara Dwyer, the manager at Lux Hotel, makes every effort to ensure that customers attempting to make phone reservations do not have to wait too long to speak with a reservation specialist. Since the hotel accepts phone reservations 24 hours a day, Barbara is especially interested in maintaining
Consider the following competing hypotheses and relevant summary statistics:Conduct this hypothesis test at the 5% significance level. State your assumptions. Hoi oilo 1 Hai olo3
Consider the following competing hypotheses and relevant summary statistics:Conduct this test at the 5% significance level. State your assumptions. Họ: olo1 Sample 1: s = 935 and n, = 14 Sample 2: s = 812 and n2 = 11
Consider the following competing hypotheses and relevant summary statistics:Assume that the two populations are normally distributed. Conduct this test at the 5% significance level. Họ: olo = 1 Hại olo#1 Sample 1: X, = 48.5, s = 18.7, and n = 10 Sample 2: X2 = 50.2, s = 12.9, and n2 = 8 %3D %3D
Use the F table to find the following probabilities.a. P(F(10,8) ≥ 3.35)b. P(F(10,8) < 0.42)c. P(F(10,8) ≥ 4.30)d. P(F(10,8) < 0.26)
Use the F table to find the value x for which:a. P(F(4,8) ≥ x) = 0.025b. P(F(4,8) ≥ x) = 0.05c. P(F(4,8) < x) = 0.025d. P(F(4,8) < x) = 0.05
The data accompanying this exercise show miles per gallon (mpg) for 25 cars.a. State the null and the alternative hypotheses in order to test whether the variance differs from 62 mpg2.b. Assuming that mpg is normally distributed, calculate the value of the test statistic.c. Find the p-value.d. Make
A realtor in Mission Viejo, California, believes that the standard deviation of house prices is more than 100 units, where each unit equals $1,000. Assume house prices are normally distributed.a. State the null and the alternative hypotheses for the test.b. Calculate the value of the test
Consider the following hypotheses:Find the p-value based on the following sample information, where the sample is drawn from a normally distributed population.a. s2 = 300; n = 25b. s2 = 100; n = 25c. Which of the above sample information enables us to reject the null hypothesis at α = 0.05? Ho: o
In order to conduct a hypothesis test for the population variance, you compute s2 = 75 from a sample of 21 observations drawn from a normally distributed population. Conduct the following tests at α = 0.10.H0 : σ2 ≤ 50; HA : σ2 > 50H0 : σ2 = 50; HA : σ2 ≠ 50
In order to construct a confidence interval for the population variance, a random sample of n observations is drawn from a normal population. Use this information to find and under the following scenarios.a. A 95% confidence level with n = 18b. A 95% confidence level with n =
Fresh numbers from the U.S. Department of Transportation suggest that fewer flights in the United States arrive on time than before. The explanations offered for the lackluster performance are understaffed airlines, a high volume of travelers, and overtaxed air traffic control. A transportation
A report suggests that business majors spend the least amount of time on course work than all other college students (The New York Times, November 17, 2011). A provost of a university decides to conduct a survey where students are asked if they study hard, defined as spending at least 20 hours per
A 2015 national survey by the Washington Post-Kaiser Family Foundation finds that there is a big gender divide between Americans when identifying as feminist or strong feminist. The results of the survey are shown in the following table. In addition, per the 2010 U.S. Census Current Population
There is a growing public support for marijuana law reform, with polls showing more than half the country is in favor of some form of marijuana legalization. However, opinions on marijuana are divided starkly along political party lines. The results of the Pew Research Center survey conducted in
According to eMarketer estimates, 88.3% of 12- to 17-year-olds had a mobile phone in 2016. Among those with mobile phones, 84.0% had smartphones. Calculate the proportion of 12-to 17-year-olds who had smartphones.
Let A and B be independent events with P(A) = 0.40 and P(B) = 0.50.a. Calculate P(A ∩ B).b. Calculate P((A ∪ B)c).c. Calculate P(A ∣ B).
Let P(A) = 0.55, P(B) = 0.30, and P(A ∩ B) = 0.10.a. Calculate P(A ∣ B).b. Calculate P(A ∪ B).c. Calculate P((A ∪ B)c).
Let P(A) = 0.65, P(B) = 0.30, and P(A ∣ B) = 0.45.a. Calculate P(A ∩ B).b. Calculate P(A ∪ B).c. Calculate P(B ∣ A).
The following table shows the annual returns (in %) for two of Putnam’s mutual funds: the Voyager Growth Fund and the George Putnam Balanced Fund.a. Calculate and interpret the covariance.b. Calculate and interpret the correlation coefficient. Year Growth Balanced 2011 -17.76 2.71 14.39 2012
Consider the following sample data:a. Calculate the covariance.b. Calculate and interpret the correlation coefficient. 12 18 20 22 25 х 25 15 20 22 27 У
Consider the following sample data:a. Calculate the covariance.b. Calculate and interpret the correlation coefficient. -2 -2 -3 -8 -9 -10 y 4) 3.
The accompanying data file shows, among other variables, median household income and median house value for the 50 states in 2010. Assume that income and house value data are bell-shaped.a. Use z-scores to determine if there are any outliers in the household income data.b. Use z-scores to determine
On average, an American professional football game lasts about three hours, even though the ball is actually in play only 11 minutes (www.sportsgrid.com, January 14, 2014). Let the standard deviation be 0.4 hour.a. Use Chebyshev’s theorem to approximate the proportion of games that last between
Suppose at the beginning of 2012 you decide to invest $1,000 in Vanguard’s European Stock Index mutual fund. The following table shows the returns (in %) for the years 2012–2015.Year . . . . . . . . . . . . . . Annual Return2012 . . . . . . . . . . . . . . 17.32013 . . . . . . . . . . . . . .
In an effort to make children’s toys safer and more tamperproof, toy packaging has become cumbersome for parents to remove in many cases. Accordingly, the director of marketing at Toys4Tots, a large toy manufacturer, wants to evaluate the effectiveness of a new packagingdesign that engineers
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 between the population proportions differs from 0.20?
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? Hoi Pi – P2 = 0 Hại Pi – P2 # 0 X1 = 300 X2 =
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? Ho: Pi – P2 = 0 HẠ: P1 – P2 # 0 X1 = 100 X2 =
A bank employs two appraisers. When approving borrowers for mortgages, it is imperative that the appraisers value the same types of properties consistently. To make sure that this is the case, the bank examines six properties (in $1,000s) that the appraisers had valued recently.a. Specify the
A sample of 35 paired observations generates the following results: d̅ = 1.3 and sD = 3.8. a. Specify the appropriate hypotheses to test if the mean difference is greater than zero. b. Calculate the value of the test statistic and the p-value. c. At the 5% significance level, can
Consider the following competing hypotheses and accompanying sample data.Assume that the populations are normally distributed with equal variances.a. Calculate the value of the test statistic and the p-value.b. At the 5% significance level, can you conclude that the difference between the two means
Thirty-three percent of children and teens in the United States are obese or overweight (Health, October 2010). A health practitioner in the Midwest collects data on 200 children and teens and finds that 84 of them are either obese or overweight.a. The health practitioner believes that the
Residents of Hawaii have the longest life expectancies in the United States, averaging 81.48 years (www.worldlifeexpectancy.com; data retrieved June 4, 2012). A sociologist collects data on the age at death for 50 recently deceased Michigan residents.a. The sociologist believes that the life
A survey finds that 17% of Americans cannot part with their landlines (The Washington Post, February 27, 2014). A researcher in the rural South collects data from 200 households and finds that 45 of them still have landlines.a. The researcher believes that the proportion of households with
In order to test if the population proportion is greater than 0.65, you draw a random sample of 200 observations and obtain a sample proportion of 0.72.a. Specify the competing hypotheses.b. Is the normality condition satisfied? Explain.c. Calculate the value of the test statistic and the
In order to test if the population proportion differs from 0.40, you draw a random sample of 100 observations and obtain a sample proportion of 0.48.a. Specify the competing hypotheses.b. Is the normality condition satisfied? Explain.c. Calculate the value of the test statistic and the p-value.d.
The data accompanying this exercise show miles per gallon (MPG).a. State the null and the alternative hypotheses in order to test whether the average MPG differs from 95.b. Calculate the value of the test statistic and the p-value.c. At α = 0.05, can you conclude that the average MPG differs from
Consider the following hypotheses:A sample of 25 observations yields a sample mean of −12. Assume that the sample is drawn from a normal population with a sample standard deviation of 4.a. Calculate the value of the test statistic.b. At the 5% significance level, is the population mean less than
Consider the following hypotheses:A sample of 16 observations yields a sample mean of 46. Assume that the sample is drawn from a normal population with a sample standard deviation of 10. a. Calculate the value of the test statistic.b. At the 5% significance level, does the population mean
An economist wants to test if the average hourly wage is less than $22. Assume that the population standard deviation is $6. a. State the null and the alternative hypotheses for the test.b. The data accompanying this exercise show hourly wages. Find the value of the test statistic and the
According to the Centers for Disease Control and Prevention (February 18, 2016), 1 in 3 American adults don’t get enough 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
A researcher wants to determine if the population mean is greater than 45. A random sample of 36 observations yields a sample mean of 47. Assume that the population standard deviation is 8.a. Specify the competing hypotheses to test the researcher’s claim.b. Calculate the value of the test
Consider the following hypotheses:A sample of 16 observations yields a sample mean of 95. Assume that the sample is drawn from a normal population with a population standard deviation of 10.a. Calculate the value of the test statistic.b. Find the p-value.c. At the 10% significance level, what is
In a report, use the above information to1. Calculate descriptive statistics to compare the returns of the mutual funds. 2. Assess reward by constructing and interpreting 95% confidence intervals for the population mean return. What assumption did you make for the interval estimates?The
A random sample of 100 observations results in 40 successes.a. What is the point estimate for the population proportion of successes?b. Construct 90% and 99% confidence intervals for the population proportion.c. Can we conclude at 90% confidence that the population proportion differs from 0.5?d.
The following table shows the annual returns (in percent) for Fidelity’s Electronics and Utilities funds.a. Derive the 99% confidence intervals for the mean returns for Fidelity’s Electronics and Utilities funds.b. What did you have to assume to make the above inferences? Electronics Year
The producer of a particular brand of soup claims that its sodium content is 50% less than that of its competitor. The food label states that the sodium content measures 410 milligrams per serving. Assume the population of sodium content is normally distributed with a standard deviation of 25
A variety of packaging solutions exist for products that must be kept within a specific temperature range. Cold chain distribution is particularly useful in the food and pharmaceutical industries. A packaging company strives to maintain a constant temperature for its packages. It is believed that
Fast bowling, also known as pace bowling, is an important component of the bowling attack in the sport of cricket. The objective is to bowl at a high speed and make the ball turn in the air and off the ground so that it becomes difficult for the batsman to hit it cleanly. Kalwant Singh is a budding
A production process is designed to fill boxes with an average of 14 ounces of cereal. The population of filling weights is normally distributed with a standard deviation of 2 ounces. Inspectors take periodic samples of 10 boxes. The following sample means are obtained.a. Construct an x̅ chart.
Major League Baseball Rule 1.09 states that “the baseball shall weigh not less than 5 or more than 5¼ ounces” (www.mlb.com). Use these values as the lower and the upper control limits, respectively. Assume the centerline equals 5.125 ounces. Periodic samples of 50 baseballs produce the
A random sample of size n = 100 is taken from a population of size N = 2,500 with mean μ = −45 and variance σ2 = 81.a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of the sample mean.b. What is the
A random sample of size n = 50 is taken from a population with mean μ = −9.5 and standard deviation σ = 2.Calculate the expected value and the standard error for the sampling distribution of thea. Sample mean.b. What is the probability that the sample mean is less than −10?c. What is the
In a report, use the sample information to1. Calculate and interpret the probability that temperature goes (a) below 2°C and (b) above 8°C using a normal distribution approximation.2. Calculate the probability that temperature goes (a) below 2°C and (b) above 8°C using a log normal distribution
In 2015, the U.S. Census Bureau reported that the median income for American households was $52,353, whereas the mean income was $71,932 (www.census.gov, data retrieved March 26, 2017). Suppose income can be represented by a lognormal variable, Y = eX, where X is normally distributed. The mean and
The mileage (in 1,000s of miles) that car owners get with a certain kind of radial tire is a random variable Y having a lognormal distribution such that Y = eX, where X is normally distributed. Let the mean and the standard deviation of the life of a radial tire be 40,000 miles and 5,000 miles,
The relief time provided by a standard dose of a popular children’s allergy medicine averages six hours with a standard deviation of two hours.a. Determine the percentage of children who experience relief for less than four hours if the relief time follows a normal distribution.b. Determine the
It is well documented that a typical washing machine can last anywhere between 5 to 12 years. Let the life of a washing machine be represented by a log normal variable, Y = eX, where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 8
The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $39,626 and the median incomeis $33,600. A demographer decides to use
Let X be exponentially distributed with μ = 1.25. Compute the following values.a. P(X < 2.3)b. P(1.5 ≤ X ≤ 5.5)c. P(X > 7)
Let X be exponentially distributed with λ = 0.5. Compute the following values.a. P(X ≤ 1)b. P(2 < X < 4)c. P(X > 10)
On average, an American professional football game lasts about three hours, even though the ball is actually in play only 11 minutes (www.sportsgrid.com, January 14, 2014). Assume that game times are normally distributed with a standard deviation of 0.4 hour.a. Find the probability that a game
Loans that are 60 days or more past due are considered seriously delinquent. The Mortgage Bankers Association reported that the rate of seriously delinquent loans has an average of 9.1% (The Wall Street Journal, August 26, 2010). Let the rate of seriously delinquent loans follow a normal
Assume that IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 16.a. What is the probability that an individual scores between 84 and 116?b. What is the probability that an individual scores less than 68?c. What is the lowest score that will place an individual in
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.
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)
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)
For a continuous random variable X with an upper bound of 4, P (0 ≤ X ≤ 2.5) = 0.54 and P (2.5 ≤ X ≤ 4) = 0.16. Calculate the following probabilities.a. P(X < 0)b. P(X > 2.5)c. P(0 ≤ X ≤ 4)
The cumulative probabilities for a continuous random variable X are P (X ≤ 10) = 0.42 and P (X ≤ 20) = 0.66. Calculate the following probabilities.a. P(X > 10)b. P(X > 20)c. P(10 < X < 20)
A portfolio has $200,000 invested in Asset X and $300,000 in Asset Y. Consider the summary measures in the following table.a. Calculate the portfolio weights for assets X and Y.b. Calculate the expected return for the portfolio.c. Calculate the standard deviation for the portfolio. Asset X Measures
A committee of 10 is to be chosen from 50 people, 25 of whom are Republicans and 25 Democrats. The committee is chosen at random.a. What is the probability that there will be five Republicans and five Democrats?b. What is the probability that a majority of the committee will be Republicans?
Find the probability that an Internal Revenue Service (IRS) auditor will catch only 4 income tax returns with illegitimate deductions if he randomly selects 5 returns from among 20 returns, of which 10 contain illegitimate deductions.
Consider the following information on the expected return for companies X and Y.a. Calculate the expected value and the standard deviation of returns for companies X and Y.b. Calculate the correlation coefficient if the covariance between X and Y is 88. Y (in %) X (in %) Probability Economy Boom
Due to the advent of tablets, American adults are watching significantly less television than they did in previous decades. In 2016, Nielsen reported that American adults are watching an average of five hours and four minutes, or 304 minutes, of television per day.a. Find the probability that an
Which of the following scenarios are likely to represent Poisson random variables?a. The number of violent crimes in New York over a six-week period.b. The number of customers of a bank manager who will default.c. The number of scratches on a 2-by-1-foot portion of a large wooden table.d. The
Which of the following probabilities are likely to be found using a Poisson distribution?a. The probability that there will be six leaks in a specified stretch of a pipeline.b. The probability that at least 10 students in a class of 40 will land a job right after graduation.c. The probability that
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 workforce?b. What is the probability that at
In 2013, only 26% of Americans had confidence in U.S. banks, which is still far below the pre-recession level of 41% reported in June 2007 (www.gallup.com, June 26, 2014). a. What is the probability that fewer than half of four Americans in 2013 have confidence in U.S. banks?b. What would have
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 randomly selected.a. What is the probability
An appliance store sells additional warranties on its refrigerators. Twenty percent of the buyers buy the limited warranty for $100 and 5% buy the extended warranty for $200. What is the expected revenue for the store from the warranty if it sells 120 refrigerators?
Calculate the expected numerical grade in Professor Underwood’s class using 4.0 for A, 3.0 for B, etc. Grade Probability 0.10 A B 0.30 0.40 0.10 0.10
After Donald Trump won the election, the consumer confidence index rose to 93.8, a sixmonth high (www.bloomberg.com, November 23, 2016). Given new economic data, an analyst believes that there is a 75% chance that the index will fall below 90 and only a 5% chance that it will rise above 95. The
Jacqueline Fibbe manages 10 employees at a small ice cream store in Beverly Farms, MA. She assigns three employees for each eight-hour shift.a. If order is not important, in how many different ways can she select three employees from the total of 10 for each eight-hour shift?b. Megan H. is one of
A horse-racing fan is contemplating the many different outcomes in an eight-horse race.a. How many different outcomes are possible if only the first three places are considered and ranking (first, second, and third) is important?b. If each of the outcomes in part a is equally likely, what is the
At a local elementary school, a principal is making random class assignments for her 8 teachers. Each teacher must be assigned to exactly one job. In how many ways can the assignments be made?
Consider the following scenarios to determine if the mentioned combination of attributes represents a union or an intersection.a. There are two courses that seem interesting to you, and you would be happy if you can take at least one of them.b. There are two courses that seem interesting to you,
Consider the following scenarios to determine if the mentioned combination of attributes represents a union or an intersection.a. A marketing firm is looking for a candidate with a business degree and at least five years of work experience.b. A family has decided to purchase Toyota or Honda.
Jane Peterson has taken Amtrak to travel from New York to Washington, DC, on six occasions, of which three times the train was late. Therefore, Jane tells her friends that the probability that this train will arrive on time is 0.50. Would you label this probability as empirical or classical? Why
Survey data, based on 65,000 mobile phone subscribers, shows that 44% of the subscribers use smartphones (Forbes, December 15, 2011). Based on this information, you infer that the probability that a mobile phone subscriber uses a smartphone is 0.44. Would you consider this probability estimate

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