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The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions

Brand names and generic products.(a) If a store always prices its generic “store brand’’ products at exactly 90% of the brand name products’ prices, what would be the correlation between these two prices? (Hint: Draw a scatterplot for several prices.)(b) If the store always prices its
Strong association but no correlation. Here is a data set that illustrates an important point about correlation:x 20 30 40 50 60 y 10 30 50 30 10(a) Make a scatterplot of y versus x.(b) Describe the relationship between y and x. Is it weak or strong? Is it linear?(c) Find the correlation between y
Change the units. Refer to Exercise 2.6 (page 67), where you changed the units to millions of dollars for education spending and to thousands for population.(a) Find the correlation between spending on education and population using the new units.(b) Compare this correlation with the one that you
Spending on education. In Example 2.3 (page 66), we examined the relationship between spending on education and population for the 50 states in the United States. Compute the correlation between these two variables.
Add the type of fuel to the plot. Refer to the previous exercise. As we did in Figure 2.6 (page 71), add the categorical variable, type of fuel, to your plot.(If your software does not have this capability, make separate plots for each fuel type. Use the same range of values for the y axis and for
Fuel efficiency and CO2 emissions. Refer to Example 2.7 (pages 70–71), where we examined the relationship between CO2 emissions and highway MPG for 1067 vehicles for the model year 2014.In that example, we used MPG as the explanatory variable and CO2 as the response variable. Let’s see if the
Use 2003 to predict 2013. Refer to the previous exercise. The data set also has times for 2003. Use the 2003 times as the explanatory variable and the 2013 times as the response variable.TTS(a) Answer the questions in the previous exercise for this setting.(b) Compare the strength of this
Time to start a business. Case 1.2 (page 23)uses the World Bank data on the time required to start a business in different countries. For Example 1.21 and several other examples that follow we used data for a subset of the countries for 2013. Data are also available for times to start in 2008.
Use a log for the radioactive decay. Refer to the previous exercise. Transform the counts using a log transformation. Then repeat parts (a) through (e) for the transformed data, and compare your results with those from the previous exercise. DECAY
A product for lab experiments. Barium-137m is a radioactive form of the element barium that decays very rapidly. It is easy and safe to use for lab experiments in schools and colleges.6 In a typical experiment, the radioactivity of a sample of barium-137m is measured for one minute. It is then
Sales and time spent on web pages. You have collected data on 1000 customers who visited the web pages of your company last week. For each customer, you recorded the time spent on your pages and the total amount of their purchases during the visit. You want to explore the relationship between these
Compare the provinces with the territories.Refer to the previous exercise. The three Canadian territories are the Northwest Territories, Nunavut, and the Yukon Territories. All of the other entries in the data set are provinces. CANADAP(a) Generate a scatterplot of the Canadian demographic data
Marketing in Canada. Many consumer items are marketed to particular age groups in a population.To plan such marketing strategies, it is helpful to know the demographic profile for different areas. Statistics Canada provides a great deal of demographic data organized in different ways.5 CANADAP(a)
More beer. Refer to the previous exercise.Repeat the exercise for the relationship between carbohydrates and percent alcohol. Be sure to include summaries of the distributions of the two variables you are studying. BEER
Brand-to-brand variation in a product.Beer100.com advertises itself as “Your Place for All Things Beer.’’ One of their “things’’ is a list of 175 domestic beer brands with the percent alcohol, calories per 12 ounces, and carbohydrates (in grams).4 In Exercises 1.56 through 1.58 (page
Companies of the world. Refer to the previous exercise. Using the questions there as a guide, describe the relationship between the numbers for 2012 and 2002. Do you expect this relationship to be stronger or weaker than the one you described in the previous exercise? Give a reason for your answer.
Companies of the world. In Exercise 1.118(page 61), you examined data collected by the World Bank on the numbers of companies that are incorporated and are listed in their country’s stock exchange at the end of the year for 2012. In Exercise 1.119, you did the same for the year 2002.3 In this
Make some sketches. For each of the following situations, make a scatterplot that illustrates the given relationship between two variables.(a) No apparent relationship.(b) A weak negative linear relationship.(c) A strong positive relationship that is not linear.(d) A more complicated relationship.
What’s wrong? Explain what is wrong with each of the following:(a) If two variables are negatively associated, then low values of one variable are associated with low values of the other variable.(b) A stemplot can be used to examine the relationship between two variables.(c) In a scatterplot, we
Transform education spending and population. Refer to Exercise 2.4(page 65). Transform the education spending and population variables using logs, and describe the distributions of the transformed variables. Compare these distributions with those described in Exercise 2.4.
Change the units.(a) Create a spreadsheet with the education spending data with education spending expressed in millions of dollars and population in thousands. In other words, multiply education spending by 1000 and multiply population by 1000.(b) Make a scatterplot for the data coded in this
Make a scatterplot.(a) Make a scatterplot similar to Figure 2.1 for the education spending data.(b) Label the four points with high population and high spending with the names of these states.
Describe the variables. Refer to the previous exercise.(a) Use graphical and numerical summaries to describe the distribution of spending.(b) Do the same for population.(c) Write a short paragraph summarizing your work in parts (a) and (b).EDSPEND DATA The most common way to display the relation
Classify the variables. Use the EDSPEND data set for this exercise. Classify each variable as categorical or quantitative. Is there a label variable in the data set?If there is, identify it.
Price versus size. You visit a local Starbucks to buy a Mocha Frappuccino®.The barista explains that this blended coffee beverage comes in three sizes and asks if you want a Tall, a Grande, or a Venti. The prices are $3.75, $4.45, and$4.95, respectively.(a) What are the variables and cases?(b)
Relationship between worker productivity and sleep. A study is designed to examine the relationship between how effectively employees work and how much sleep they get. Think about making a data set for this study.(a) What are the cases?(b) Would your data set have a label variable? If yes, describe
Simulated observations. Most statistical software packages have routines for simulating values having specified distributions. Use your statistical software to generate 30 observations from the N(25, 4)distribution. Compute the mean and standard deviation x and s of the 30 values you obtain. How
What influences buying? Product preference depends in part on the age, income, and gender of the consumer. A market researcher selects a large sample of potential car buyers. For each consumer, she records gender, age, household income, and automobile preference. Which of these variables are
Grading managers. Some companies “grade on a bell curve’’ to compare the performance of their managers. This forces the use of some low performance ratings so that not all managers are graded “above average.’’ A company decides to give A’s to the managers and professional workers who
What colors sell? Customers’ preference for vehicle colors vary with time and place. Here are data on the most popular colors in 2012 for North America.Color (Percent)White 24 Black 19 Silver 16 Gray 15 Red 10 Blue 7 Brown 5 Other 4 Use the methods you learned in this chapter to describe these
Companies of the world. Refer to the previous exercise. Examine the data for 2002, and compare your results with what you found in the previous exercise. Note that some cases have missing values for this variable. Your summary should include information about this characteristic of these data.
Beer breweries. Refer to Exercise 1.115.BEER Describe the distribution of the variable brewery using the methods you have learned in this chapter.1.118 Companies of the world. The Word Bank collects large amounts of data related to business issues from different countries. One set of data records
Beer carbohydrates. Refer to the previous exercise. BEER Describe the distribution of the variable carbohydrates using the methods you have learned in this chapter.Note that some cases have missing values for this variable. Your summary should include information about this characteristic of these
Beer variables. Refer to Exercises 1.56 through 1.58 (page 36). The data set BEER contains values for five variables: (1) brand; (2) brewery;(3) percent alcohol; (4) calories per 12 ounces; and(5) carbohydrates in grams. BEER(a) Identify each of these variables as categorical or quantitative.(b) Is
Best brands revenue. Refer to the Exercise==1.112. Describe the distribution of the variable revenue using the methods you have learned in this chapter.Your summary should include information about this characteristic of these data. BRANDS
Best brands industry. Refer to the previous exercise. BRANDS Describe the distribution of the variable industry using the methods you have learned in this chapter.
Best brands variables. Refer to Exercises 1.53 and 1.54 (page 36). The data set BRANDS contains values for seven variables: (1) rank, a number between 1 and 100 with 1 being the best brand, etc.; (2)company name; (3) value of the brand, in millions of dollars; (4) change, difference between last
Another look at marketing products for seniors in Canada. In Exercise 1.32 (page 23), you analyzed data on the percent of the population over 65 in the 13 Canadian provinces and territories. Those with relatively large percents might be good prospects for marketing products for seniors. In
Another look at T-bill rates. Refer to Example 1.12 with the histogram in Figure 1.6(page 13), Example 1.20 with the time plot in Figure 1.12 (page 20), and Example 1.41 with the normal quantile plot in Figure 1.29(page 53). These examples tells us something about the distribution T-bill rates and
Flopping in the 2014 World Cup. Soccer players are often accused of spending an excessive amount of time dramatically falling to the ground followed by other activities, suggesting that a possible injury is very serious. It has been suggested that these tactics are often designed to influence the
Jobs for business majors. What types of jobs are available for students who graduate with a business degree? The website careerbuilder.com lists job opportunities classified in a variety of ways. A recent posting had 25,120 jobs. The following table gives types of jobs and the numbers of postings
Gross domestic product per capita. Refer to the previous exercise. The data set also contains the gross domestic product per capita calculated by dividing the gross domestic produce by the size of the population for each country. BESTBUS(a) Generate a histogram and a normal quantile plot for these
Trade balance. Refer to Exercise 1.49(page 35) where you examined the distribution of trade balance for 145 countries in the best countries for business data set. Generate a histogram and a normal quantile plot for these data. Describe the shape of the distribution and whether or not the normal
Normal random numbers. Use software to generate 100 observations from the standard Normal distribution. Make a histogram of these observations.How does the shape of the histogram compare with a Normal density curve? Make a Normal quantile plot of the data. Does the plot suggest any important
Deciles of Normal distributions. The deciles of any distribution are the 10th, 20th, . . . , 90th percentiles. The first and last deciles are the 10th and 90th percentiles, respectively.(a) What are the first and last deciles of the standard Normal distribution?(b) The weights of 9-ounce potato
Quartiles of Normal distributions. The median of any Normal distribution is the same as its mean. We can use Normal calculations to find the quartiles for Normal distributions.(a) What is the area under the standard Normal curve to the left of the first quartile? Use this to find the value of the
Length of pregnancies. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.(a) What percent of pregnancies last fewer than 240 days(that is, about 8 months)?(b) What percent of
Use Table A or software. Consider a Normal distribution with mean 200 and standard deviation 20.(a) Find the proportion of the distribution with values between 190 and 220. Illustrate your calculation with a sketch.(b) Find the value of x such that the proportion of the distribution with values
Use Table A or software. Use Table A or software to find the value of z for each of the following situations. In each case, sketch a standard Normal curve and shade the area representing the region.(a) Twelve percent of the values of a standard Normal distribution are greater than z.(b) Twelve
Use Table A or software. Use Table A or software to find the proportion of observations from a standard Normal distribution that falls in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.(a) z ≤ −2.10(b) z ≥ −2.10(c) z >
Uniform random numbers. Use software to generate 100 observations from the distribution described in Exercise 1.72 (page 41). (The software will probably call this a “uniform distribution.’’)Make a histogram of these observations. How does the histogram compare with the density curve in
Length of pregnancies. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. Use the 68–95–99.7 rule to answer the following questions.(a) Between what values do the lengths of
Exploring Normal quantile plots.(a) Create three data sets: one that is clearly skewed to the right, one that is clearly skewed to the left, and one that is clearly symmetric and mound-shaped. (As an alternative to creating data sets, you can look through this chapter and find an example of each
Visualizing the standard deviation. Figure 1.34 shows two Normal curves, both with mean 0. Approximately what is the standard deviation of each of these curves?
Assign more grades. Refer to the previous exercise. The grading policy says that the cutoffs for the other grades correspond to the following:the bottom 5% receive an F, the next 15% receive a D, the next 35% receive a C, and the next 30%receive a B. These cutoffs are based on the N(72,
Total scores for accounting course. Following are the total scores of 10 students in an accounting course: ACCT 62 93 54 76 73 98 64 55 80 71 Previous experience with this course suggests that these scores should come from a distribution that is approximately Normal with mean 72 and standard
Data from Mexico. Refer to the previous exercise.A similar study in Mexico was conducted with 31 women and 20 men. The women averaged 14,704 words per day with a standard deviation of 6215. For men, the mean was 15,022 and the standard deviation was 7864.(a) Answer the questions from the previous
Do women talk more? Conventional wisdom suggests that women are more talkative than men. One study designed to examine this stereotype collected data on the speech of 42 women and 37 men in the United States.30(a) The mean number of words spoken per day by the women was 14,297 with a standard
Gross domestic product. Refer to Exercise 1.46, where we examined the gross domestic product of 189 countries. GDP(a) Compute the mean and the standard deviation.(b) Apply the 68–95–99.7 rule to this distribution.(c) Compare the results of the rule with the actual percents within one, two, and
Know your density. Sketch density curves that might describe distributions with the following shapes.(a) Symmetric, but with two peaks (that is, two strong clusters of observations).(b) Single peak and skewed to the left.
The effect of changing the standard deviation.(a) Sketch a Normal curve that has mean 20 and standard deviation 5.(b) On the same x axis, sketch a Normal curve that has mean 20 and standard deviation 2.(c) How does the Normal curve change when the standard deviation is varied but the mean stays the
Sketch some Normal curves.(a) Sketch a Normal curve that has mean 30 and standard deviation 4.(b) On the same x axis, sketch a Normal curve that has mean 20 and standard deviation 4.(c) How does the Normal curve change when the mean is varied but the standard deviation stays the same?
Find the error. Each of the following statements contains an error. Describe the error and then correct the statement.(a) The 68–95–99.7 rule applies to all distributions.(b) A normal distribution can take only positive values.(c) For a symmetric distribution, the mean will be larger than the
Find the error. Each of the following statements contains an error. Describe the error and then correct the statement.(a) A density curve is a mathematical model for the distribution of a categorical variable.(b) The area under the curve for a density curve is always greater than the mean.(c) If a
Fuel efficiency. Figure 1.31 is a Normal quantile plot for the fuel efficiency data. We looked at these data in Example 1.28. A histogram was used to display the distribution in Figure 1.17 (page 39). This distribution is approximately Normal.(a) How is this fact displayed in the Normal quantile
Length of time to start a business. In Exercise 1.33, we noted that the sample of times to start a business from 25 countries contained an outlier.For Suriname, the reported time is 208 days. This case is the most extreme in the entire data set. Figure 1.30 shows the Normal quantile plot for all
Find the score that 70% of students will exceed. Consider the ISTEP scores, which are approximately Normal, N(572, 51). Seventy percent of the students will score above x on this exam. Find x.
What score is needed to be in the top 25%? Consider the ISTEP scores, which are approximately Normal, N(572, 51). How high a score is needed to be in the top 25% of students who take this exam?
Find another proportion. Use the fact that the ISTEP scores are approximately Normal, N(572, 51). Find the proportion of students who have scores between 500 and 650. Use pictures of Normal curves similar to the ones given in Example 1.35 (page 47) to illustrate your calculations.
Find the proportion. Use the fact that the ISTEP scores from Exercise 1.76(page 44) are approximately Normal, N(572, 51). Find the proportion of students who have scores less than 620. Find the proportion of students who have scores greater than or equal to 620. Sketch the relationship between
SAT versus ACT. Emily scores 650 on the Mathematics part of the SAT. The distribution of SAT scores in a reference population is Normal, with mean 500 and standard deviation 100. Michael takes the American College Testing (ACT) Mathematics test and scores 28. ACT scores are Normally distributed
Use the 68–95–99.7 rule. Refer to the previous exercise. Use the 68–95–99.7 rule to give a range of scores that includes 99.7% of these students.
Test scores. Many states have programs for assessing the skills of students in various grades. The Indiana Statewide Testing for Educational Progress(ISTEP) is one such program.26 In a recent year 76,531, tenth-grade Indiana students took the English/language arts exam. The mean score was 572, and
More on young men’s heights. The distribution of heights of young men is approximately Normal with mean 69 inches and standard deviation 2.5 inches.Use the 68–95–99.7 rule to answer the following questions.(a) What percent of these men are taller than 74 inches?(b) Between what heights do the
Heights of young men. Product designers often must consider physical characteristics of their target population. For example, the distribution of heights of men aged 20 to 29 years is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Draw a Normal curve on which this mean
Three curves. Figure 1.21 displays three density curves, each with three points marked. At which of these points on each curve do the mean and the median fall?
A uniform distribution. Figure 1.20 displays the density curve of a uniform distribution. The curve takes the constant value 1 over the interval from 0 to 1 and is 0 outside that range of values. This means that data described by this distribution take values that are uniformly spread between 0 and
A symmetric curve. Sketch a density curve that is symmetric but has a shape different from that of the curve in Figure 1.18(a) (page 40).
Another skewed curve. Sketch a curve similar to Figure 1.18(b) for a leftskewed density curve. Be sure to mark the location of the mean and the median.
A different type of mean. The trimmed mean is a measure of center that is more resistant than the mean but uses more of the available information than the median. To compute the 5% trimmed mean, discard the highest 5% and the lowest 5% of the observations, and compute the mean of the remaining 90%.
Imputation. Various problems with data collection can cause some observations to be missing.Suppose a data set has 20 cases. Here are the values of the variable x for 10 of these cases:27 16 2 12 22 23 9 12 16 21 The values for the other 10 cases are missing. One way to deal with missing data is
A standard deviation contest. You must choose four numbers from the whole numbers 10 to 20, with repeats allowed.(a) Choose four numbers that have the smallest possible standard deviation.(b) Choose four numbers that have the largest possible standard deviation.(c) Is more than one choice possible
A skewed distribution. Sketch a distribution that is skewed to the left. On your sketch, indicate the approximate position of the mean and the median.Explain why these two values are not equal.
Salary increase for the owners. Last year, a small accounting firm paid each of its five clerks$40,000, two junior accountants $75,000 each, and the firm’s owner $455,000.(a) What is the mean salary paid at this firm? How many of the employees earn less than the mean? What is the median
Returns on Treasury bills.Figure 1.16(a) (page 34) is a stemplot of the annual returns on U.S. Treasury bills for 50 years. (The entries are rounded to the nearest tenth of a percent.)(a) Use the stemplot to find the five-number summary of T-bill returns.(b) The mean of these returns is about
x and s are not enough. The mean x and standard deviation s measure center and spread but are not a complete description of a distribution. Data sets with different shapes can have the same mean and standard deviation. To demonstrate this fact, find x and s for these two small data sets. Then make
Don’t change the median. Place five observations on the line by clicking below it.(a) Add one additional observation without changing the median. Where is your new point?(b) Use the applet to convince yourself that when you add yet another observation (there are now seven in all), the median does
Extreme observations. Place three observations on the line by clicking below it—two close together near the center of the line and one somewhat to the right of these two.(a) Pull the rightmost observation out to the right. (Place the cursor on the point, hold down a mouse button, and drag the
Mean 5 median? Place two observations on the line by clicking below it. Why does only one arrow appear?
Discovering outliers. Whether an observation is an outlier is a matter of judgment. It is convenient to have a rule for identifying suspected outliers. The 1.5 3 IQR rule is in common use:1. The interquartile range IQR is the distance between the first and third quartiles, IQR = Q3 − Q1. This is
Calories in beer. Refer to the previous two exercises. The data set also lists calories per 12 ounces of beverage.(a) Analyze the data and summarize the distribution of calories for these 175 brands of beer.(b) In Exercise 1.56, you identified one brand of beer as an outlier. To what extent is this
Outlier for alcohol content of beer. Refer to the previous exercise.(a) Calculate the mean with and without the outlier. Do the same for the median. Explain how these values change when the outlier is excluded.(b) Calculate the standard deviation with and without the outlier. Do the same for the
The alcohol content of beer. Brewing beer involves a variety of steps that can affect the alcohol content. A website gives the percent alcohol for 175 domestic brands of beer.24(a) Use graphical and numerical summaries of your choice to describe the data. Give reasons for your choice.(b) The data
Salaries of the chief executives. According to the May 2013 National Occupational Employment and Wage Estimates for the United States, the median wage was $45.96 per hour and the mean wage was$53.15 per hour.23 What explains the difference between these two measures of center?
Advertising for best brands. Refer to the previous exercise. To calculate the value of a brand, the Forbes website uses several variables, including the amount the company spent for advertising. For this exercise, you will analyze the amounts of these companies spent on advertising, reported in
Apple is the number one brand. A brand is a symbol or images that are associated with a company.An effective brand identifies the company and its products. Using a variety of measures, dollar values for brands can be calculated.22 The most valuable brand is Apple, with a value of $104.3 million.
Variability of an agricultural product. A quality product is one that is consistent and has very little variability in its characteristics. Controlling variability can be more difficult with agricultural products than with those that are manufactured. The following table gives the individual
Create a data set. Create a data set that illustrates the idea that an extreme observation can have a large effect on the mean but not on the median.
GDP Growth for 145 countries. Refer to the previous two exercises. Another variable that Forbes uses to rank countries is growth in gross domestic product, expressed as a percent.(a) Use graphical summaries to describe the distribution of the growth in GDP for these countries.(b) Give the names of
What do the trade balance graphical summaries show? Refer to the previous exercise.(a) Use graphical summaries to describe the distribution of the trade balance for these countries.(b) Give the names of the countries that correspond to extreme values in this distribution.(c) Reanalyze the data

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