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business statistics

Questions and Answers of Business Statistics

Closer examination of the miles data from the Porter project (see For Example: “Analyzinga one-way design for Ottawa–Toronto f lights”) shows that only about 5% of the students overall actually
You decide to implement the simple one-factor completely randomized design, sending out four offers (Coupon, Card, Movie, or No Offer) to 4000 students each (see For Example: “Designing an
Continuing from For Example: “Experimental design principles for Ottawa–Torontof lights,” you’re considering splitting up the students into two groups before mailingthe offers: those who live
Explain how the four principles of experimental design are used in the Porter experiment described For Example: “A marketing experiment for Ottawa– Toronto flights.”
Having discovered that most student passengers on the Porter Ottawa–Toronto routeuse the free internet service in the airport lounges (see For Example: “Observationalstudies for Ottawa–Toronto
Porter offers flights to and from the Island airport in Toronto, providing faster access to the downtown area than Pearson International Airport, which is farther from the city centre. Porter’s
The owner of the car dealership is curious about the maximum discount his salespeople are willing to give to customers. In particular, two of his salespeople, Frank and Nikita, seem to have very
We concluded in For Example: “The t-test for the difference of two mean car discounts” that, on average, women receive a larger discount than men at the car dealership. How big is the difference,
“The t-test for the difference of two mean car discounts,” we rejected the null hypothesis that the mean discount received by men and women is the same. Here are the histograms of the discounts
The owner of a large car dealership wants to understand the negotiation process for buying a new car. Cars are given a “sticker price,” but a potential buyer may negotiate a better price. The
From 58 randomly selected retail sales, an analyst finds that the mean amount spent is \($26.05\) with a standard deviation of \($10.20\) and is approximately Normally distributed. Test the
Researchers purchased whole farmed salmon at random from 51 farms in eightregions in six countries (see For Example: “Finding a confidence interval for the meancontaminant levels in fish”). The
Suppose that a year later, a full accounting of all the Smart Wool transactions (see For Example: “The reasoning of hypothesis tests about website customers”) finds that 26.5% of visits resulted
Survey companies like Nanos Research often survey about 1000 people in order toget a narrow standard deviation on their results and hence significant results. To seethe effect of using a much smaller
Find the critical z value for the Smart Wool hypothesis (see For Example:“The reasoning of hypothesis tests about website customers”) using a = 0.05 and show that the same decision would have
The analyst at SmartWool (see For Example: “Setting the a level for website customers”) makes another change to the website, puts it online, selects 200 recent web visits at random, and finds
Following from For Example: “Conclusions about website customersfrom P-values,” the manager of the analyst at SmartWool wants her to compare an alevel of 0.05 with an a level of 0.01 for her
SmartWool, an online vendor of fancy woolen ski mitts, recently redesigned its website, and analysts at Smart Wool want to know if the proportion of visits resulting in a sale has changed since the
The manager in For Example: “The distribution of a sample proportion of retail customers”also examines the amount spent by customers using the self-checkout stations.He finds that the
The analyst conducting the Rogers survey in For Example: “Sampling distribution forproportions of telecommunications customers” says that, unfortunately, only 20 of thecustomers he tried to
Rogers provides cable, phone, and internet services to customers, some of whom subscribe to “packages” including several services. Nationwide, suppose that 30% of Rogers customers are “package
A supermarket has installed “self-checkout” stations that allow customers to scan and bag their own groceries. These are popular, but because customers occasionally encounter a problem, a staff
The Charlevoix Seismic Zone (CSZ) is the most seismically active region of eastern Canada. Earthquakes of magnitude 6.0 and over occur once every 52.4 years on average. The last one occurred in 1925.
The Cyclically Adjusted Price/Earnings ratio (CAPE10) smooths out short-term f luctuations in the price/earnings ratio of companies traded on the stock market and is used by some investors as an
Suppose an MBA program says it admits only people with GMAT scores among the top 10%. How high a GMAT score does it take to be eligible?
Assuming the GMAT scores are nearly Normal with a mean of 500 and a standard deviation of 100, what proportion of GMAT scores falls between 450 and 600?
The Graduate Management Admission Test (GMAT) has scores from 200 to 800.Scores are supposed to follow a distribution that is roughly unimodal and symmetricand is designed to have an overall mean of
The Charlevoix Seismic Zone (CSZ) is the most seismically active region of easternCanada. Earthquakes of magnitude 6.0 and over occur once every 52.4 years on average.The last one occurred in 1925.
A venture capital firm has a list of potential investors who have previously invested innew technologies. On average, these investors invest in about 5% of the opportunitiespresented to them. A new
You are considering investing \($1000\) into one or possibly two different investment funds. Historically, each has delivered 5% a year in profit with a standard deviation of 3%. So, a \($1000\)
Calculating the expected value of a lottery ticket,” we found the expected gain per ticket to be -\($2.10.\) What is the standard deviation? What does it say about your chances in the lottery?
A fundraising lottery offers 500 tickets for \($3\) each. If the grand prize is \($250\) and four second prizes are \($50\) each, what is the expected value of a single ticket? (Don’t count the
Bob is 70% sure that Helen should be promoted to a management position. In order to increase the probability of making the right decision, he sends her for a psychological test. The test isn’t
A recent Ontario highway safety study found that in 77% of all accidents the driverwas wearing a seat belt. Accident reports indicated that 92% of those drivers escapedserious injury (defined as
Using the table from For Example: “Marginal probabilities for retail purchases,” if a customer purchases a fashion light, what is the probability that the customer is a woman?
Lee suspects that men and women make different kinds of purchases at Lee’s Lights(see For Example: “Using the General Addition Rule for retail purchases”). The tableshows the purchases made by
Lee notices that when two customers enter the store together, their behaviour isn’t independent. In fact, there’s a 20% chance they’ll both make a purchase.QUESTION:When two customers enter the
Some customers prefer to see the merchandise in the store but then make their purchaselater using Lee’s Lights’s new internet site. Tracking customer behaviour, Leedetermines that there’s a 9%
Lee knows that the probability that a customer will make a purchase is 30%.QUESTION:If we can assume that customers behave independently, what is the probability that the next two customers entering
Lee’s Lights sells lighting fixtures. Some customers are there only to browse, so Lee records the behaviour of all customers for a week to assess how likely it is that a customer will make a
Consider the relationship between a company’s Assets and its Sales as reported inannual financial statements. Here’s a scatterplot of those variables for 79 of the largestcompanies together with
Find and interpret the R2 for the regression found in For Example: “A linear model for retail expansion across Canada”.
Here is a scatterplot of the residuals for the linear model found in For Example: “A linear model for retail expansion across Canada” plotted against the predicted values:QUESTION: Show how the
As a retailer expands across Canada, its sales increase. Here are some data on sales and number of stores over the last 10 years, including the means, standard deviations, and correlation
“Finding the correlation coefficient for cycling accidents”Cycle/car accidents are a serious concern for insurance companies.Here are data on the mean age of cyclists killed each year in the
When examining the ages of victims in cycle/car accidents, why does it make the most sense to plot Year on the x-axis and Mean Age on the y-axis?
Cycle/car accidents are a serious concern for insurance companies. About 53,000 cyclists have died in traffic crashes in the United States since 1932. Demographic information such as this is often
Every year Fortune magazine publishes a list of the 100 best companies to work for. One statistic often looked at is the average annual pay for the most common job title at the company. Here’s a
Advertising. A company that distributes a variety of pet foods is planning its next advertising campaign.Since different publications are read by different market segments, the company would like to
Ipsos’s Canadian media landscape. This study captures the daily activities of Canadians to show marketers what opportunities they have to present their messages. It finds that, in an average day,
Downtown parking. In the downtown area of a city, a condo building has 100 households. Eighteen percent of these households have 1 car and 4% have 2 cars. The rest have no cars.Represent the
Department store. A department store is planning its next advertising campaign. Since different publications are read by different market segments, it would like to know if it should be targeting
Canadian airports. Canadian governments have leased their major airports to a private sector interest that needs to make a profit from their operation. Apart from fees from airlines, non-aeronautical
MBAs, part 2.A university reported the following data on the gender of its students in its two MBA programs:Gender Type Full-Time Part-Time Total Men 116 66 182 Women 48 38 86 Total 164 104 268a)
Canadian reportable accidents. Accidents in Canada involving dangerous goods must be reported to the government and are recorded by Statistics Canada. Set out below is a summary of the number of such
Movie ratings. The movie ratings system is a voluntary system operated jointly by the Motion Picture Association of America (MPAA) and the National Association of Theatre Owners (NATO). The ratings
MBAs, part 1.A survey of the entering MBA students at a university in Canada classified the country of origin of the students, as seen in the table.Origin MBA Program Two-Year MBA Evening MBA Total
Transport injuries in Canada. The table below shows the number of deaths in Canada from some forms of transport accidents by gender, in 2016:Males Females Pedestrian 204 154 Pedal Cyclist 51 18
New product. A company started and managed by Business students is selling campus calendars. The students have conducted a market survey with the various campus constituents to determine sales
Stock performance. The following table displays information for 470 of the S&P 500 stocks on how their oneday change on one specific day compared with their year to date performance up to that
Printing textbooks. A publisher sells textbooks on a broad range of subjects to Canadian university students.The students purchase online access to the book and associated materials, and can
International unemployment rates. The table below gives the unemployment rate according to stats.oecd.org for selected countries. Create a graphical representation of these data that facilitates
International comparison of government debt. The government net financial liabilities as a percentage of GDP is given in the table below for selected countries according to stats.oecd.org. Present
Nuclear reactors around the world. The number of nuclear reactors that were operational in selected countries in 2014 is given in the table below, together with the number of additional nuclear
International natural gas reserves and resources. Countries divide natural gas into reserves (the amount economically extractable at current prices) and resources (the amount technically extractable
Multinational exports. The exports of a multinational company from four of the countries in which it operates are given in the table.Country Debt Britain £1.4 bn Canada 1.2 $CDN bn Japan 10.5 ¥ bn
International comparison of government debt. The government net financial liabilities as a percentage of GDP is given in the table below for selected countries according to stats.oecd.org. Present
Nuclear reactors around the world. The number of nuclear reactors that were operational in selected countries in 2014 is given in the table below, together with the number of additional nuclear
International natural gas reserves and resources. Countries divide natural gas into reserves (the amount economically extractable at current prices) and resources (the amount technically extractable
Multinational exports. The exports of a multinational company from four of the countries in which it operates are given in the table.Country Debt Britain £1.4 bn Canada 1.2 $CDN bn Japan 10.5 ¥ bn
Importance of power. In the same survey discussed in Exercise 27, GfK Roper Consulting also asked, “How important is having control over people and resources to you?” The percentages of people
Importance of wealth. GfK Roper Reports Worldwide surveyed people in 2004, asking them, “How important is acquiring wealth to you?” The percentage of people who responded that it was of more than
Winter Olympics. Twenty-one countries won gold medals in the 2014 Winter Olympics. The following table lists the countries, along with the total number of medals each won:a) Try to make a display of
Environmental hazard. Data from the International Tanker Owners Pollution Federation Limited (www.itopf.com) give the cause of spillage for small and large oil tanker accidents for 1970–2017. Draw
Canadian election results, part 2.In the 2015 Canadian federal election, the number of seats and the percentage of votes were divided among the parties as follows:a) Draw a graph of this data that
Small business productivity. A survey asked small business owners. “How difficult or easy do you think it will be for your company to obtain credit when you need it?” The business owners answered
Mattel. In a recent annual report, Mattel Inc. reported that its domestic market sales were broken down as follows:49.6% Mattel Girls and Boys brand; 36.1% Fisher-Price brand; and the rest of
Ontario university funding. In Ontario, the Ministry of Advanced Education and Skills Development (MAESD)partially funds universities, plus a large proportion of the funding comes from other sources,
Canadian election results, part 1.In the 2015 Canadian federal election, the number of seats was divided among the parties as shown in the table in the next column. The Liberals won the election,
Plastic pollution. Of the 8.3bn tonnes of plastic produced during the past 65 years, 2.5bn is still in use and 5.8bn was used once. After that single use, 0.1bn was recycled and is part of the 2.5bn
World market share, part 3.Here’s a pie chart of the data in Exercise 16:a) Which display of these data is best for comparing the market shares of these companies? Explain.b) Does Mountain Dew or
Market share, part 2.Here’s a bar chart of the data in Exercise 15:a) Compared to the pie chart in Exercise 15, which is better for displaying the relative portions of market share? Explain.b) What
World market share, part 1.The Wall Street Journal article described in Exercise 15 also indicated the market share for leading brands of carbonated beverages worldwide. The following bar chart
U.S. market share. An article in The Wall Street Journal(March 18, 2011) reported the 2010 U.S. market share of leading sellers of carbonated drinks, as summarized in the following pie chart:a) Is
Tables in the news, part 2.Find a contingency table of categorical data from a business publication (e.g., The Economist, The Globe and Mail, The Wall Street Journal, etc.).a) Is the table clearly
Tables in the news, part 1.Find a frequency table of categorical data from a business publication (e.g., The Economist, The Globe and Mail, The Wall Street Journal, etc.).a) Is the table clearly
Graphs in the news, part 2.Find a pie chart of categorical data from a business publication (e.g., The Economist, The Globe and Mail, The Wall Street Journal, etc.).a) Is the graph clearly
Graphs in the news, part 1.Find a bar graph of categorical data from a business publication (e.g., The Economist, The Globe and Mail, The Wall Street Journal, etc.).a) Is the graph clearly
For the table in Exercise 8,a) Find the column percentages.b) Looking at the column percentages in (a), does the distribution of how many times someone has seen the movie look the same for each age
For the table in Exercise 7,a) Find the column percentages.b) Looking at the column percentages in (a), does the tenure distribution (how long the employee has been with the company) for each
In addition to their age levels, the movie audiences in Exercise 2 were asked if they had seen the movie before(Never, Once, More than Once). Here’s a table showing the responses by age group:a)
From Exercise 1, we also have data on how long each person has been with the company (tenure) categorized into three levels: less than one year, between one and five years, and more than five years.
For the educational levels described in Exercise 1:a) Write two to four sentences summarizing the distribution.b) What conclusions, if any, could you make about the educational levels of employees at
As a member of the human resource group of your company, you are asked to summarize the educational levels of the 512 employees in your division. From company records, you find that 164 have no
An established Canadian bank wanted to get its employees’ opinions about an internal reorganization it had implemented in order to compete with new financial institutions (sometime called FinTech
During the Canadian census, most Canadians complete a “Short Form” which is the government’s primary source of demographic data. Some Canadians are selected at random to complete a “Long
A manufacturing company employs 14 project managers, 48 forepersons, and 377 labourers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct
Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments for at most 120 orders each
Improve the following survey questions by rephrasing them. State what was wrong with the original question.a) How small was your Airbnb room?b) Should parents concerned about their child's safety buy
A market research company wants to survey commercial building managers as to whether they plan to install solar power on the roof of their building in the next five years. The profitability of such

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