Questions and Answers of Applied Statistics And Multivariate

You have a hunch that the product sales mentioned in Exercise 5 (Chap. 3) are not determined by price alone. So you perform a multivariate regression using Excel (or statistics software like SPSS).
Of the 25 employees at a mid-sized company, five are fine with longer opening hours. A journalist investigating attitudes towards the new opening hours selects six employees from the company at
Inge knows 50 hairstylists. How great is the likelihood that at least two of the 50 hairstylists have the same birthday? This is known as the birthday paradox.
Use Stata, SPSS, or Excel for the questionnaire in Fig. 2.1, and enter the data from Fig. 3.1. Allow for missing values in the dataset.Figure 2.1Figure 3.1 Gender: male ☐ female Age: Body
For each of the following statistical units, provide traits and trait values:(a) Patient cause of death(b) Length of university study(c) Alcohol content of a drink
For each of the following traits, indicate the appropriate level of measurement:(a) Student part-time jobs(b) Market share of a product between 0% and 100%(c) Students’ chosen programme of study(d)
A spa resort conducts a survey of their hot spring users, asking how often they visit the spa facility. This survey results in the following absolute frequency data:1. Identify the trait (level of
Supposed the Fig. 3.29 appears in a market research study. What can be said about it? 2 1.5 1 0.5 1972 Produced vehicles in UK [in millions of vehicles] 1980 1982 HLE 1986 1987 1988
Using the values 4, 2, 5, 6, 1, 6, 8, 3, 4, and 9, calculate:(a) The median(b) The arithmetic mean(c) The mean absolute deviation from the median(d) The empirical variance(e) The empirical standard
You’re employed in the marketing department of an international car dealer. Your boss asks you to determine the most important factors influencing car sales. You receive the following data:(a) What
A used car market contains 200 vehicles across the following price categories:(a) Draw a histogram for the relative frequencies. How would you have done the data acquisition differently?(b) Calculate
The arithmetic mean x = 10 and the empirical standard deviation Semp = 2 were calculated for a sample (n = 50). Later, the values x51 = 18 und x52 = 28 were added to the sample. What is the new
One-hundred customers were randomly selected for an experiment measuring the effect of music on the amount of money people spend in a supermarket. One half of the customers shopped on days when no
Unions and employers sign a 4-year tariff agreement. In the first year, employees’ salaries increase by 4%, in the second year by 3%, in the third year by 2%, and in the fourth year by 1%.
A company measures customer satisfaction in three regions, producing the following crosstab:(a) What percentage of respondents answering “good” come from region 3?(b) Interpret the strength of
You are given the task of sampling the household size of customers at a grocery store and the number of bananas they buy.(a) You collect 150 observations. The relative frequency is f(x = 4jy = 2) =
A company has sold €30 m worth of goods over the last 3 years. In the first year, they sold €8 m, in the second year €7 m, and in the third year €15 m. What is the concentration of sales over
(a) Based on the data in Exercise 5 in Chap. 3, you conjecture that price is the decisive variable determining sales. Use a scatterplot to verify this hypothesis.(b) Determine the standard deviation
A PISA study assesses the performance of students in 14 German states. The variables scientific literacy (x) and reading comprehension (y) yield the following information:(a) What is the (unweighted)
You want to find out whether there is an association between the quantity of customer purchases ( y) and customer income € (x). For 715 customers, you calculate a covariance between income and
The newspaper Stupid Times published a study on the connection between the number of books people have read (x) and the serious colds they have had. The study—which relied on a mere five
Researchers investigated the market share of a product called Funny in a variety of retail stores. A few stores ran advertisements during certain weeks. Researchers assemble the following data:The
For a particular brand of potato chips, a market research institute determines a high correlation coefficient—r = (0.7383)—between sales and price. Accidentally, they also discover a weak
Inge is a sales representative for a shampoo brand. She plans to visit ten hairstylists who work at different salons as she makes her daily rounds.(a) How many possible routes can Inge take?(b) Of
Twenty companies have advertised a job opening. There are 20 people seeking work through the job centre who qualify for the positions. Sixteen applications are from women and four from men. If the
A marketing executive decides to limit his company’s ads to three channels. Under consideration are the German networks ARD, ZDF, RTL, SAT1, and PRO 7.(a) How many combinations of three channels
(a) Ten horses take part in a horse race. How many possibilities exist for picking the top three horses in the order they finish?(b) A track and field club has six equally fast sprinters from which
A cigarette dispenser has 12 slots and 10 different brands. How many ways are there to stock the dispenser, if the number of packages of a brand is all that matters?
One-hundred students attend a statistics lecture. For the exam, students have two practice exams available. Fifty per cent of the students complete practice exam #1. Fifteen percent complete practice
Following the introduction of the euro, counterfeiters expand their activities. The probability that a euro bill is counterfeit is 0.5%. Retailers are vigilant and install machines at the cash
From experience you know that 78% of students pass the statistics exam. Of those who pass the exam, 67% go on holiday after the results are posted. Those who fail usually want to study some more, but
A finish inspection at a car manufacturer paint shop assigns one of three scores per car body:A1 means perfect;A2 only streaks are present;A3 only air bubbles are present;A4 streaks and air bubbles
A market research institute determines that 80% of all newly introduced products flop in a certain branch. But even when the decision to mass produce a new product is based on the results of a test
Three machines A, B, and C produce 50%, 30%, and 20% of the entire factory output, respectively. The reject rates for the machines are 3%, 4%, and 5%, respectively.(a) Represent the individual
True to the motto “just in time”—the principle of flexible and quick response—a car parts supplier keeps only a small number of injection pumps in stock. Within an hour of receiving an order
The local train leaves the station once every 15 min. What is the probability that a randomly arriving passenger will have to wait more than 10 min?
The student Erwin wants to start his car. He knows that the battery has a 98% probability of being in working order and that each of the four spark plugs has a 95% probability of firing. He also
Of all the business students at Pforzheim University, 45% have been to Spain (including the Balearic Islands and the Canary Islands) and 23% have been to Portugal. 11% have been to both Portugal and
A delivery of N televisions contains M B-grade devices. To estimate the share of Bgrade televisions in the batch, a sample n is taken.(a) What is the distribution of B-grade televisions if each unit
In the production of a certain component, the share of rejected items is θ = 0.01. A researcher selects a random sample of n = 100 from the assembly line. Calculate the probability that there is no
The calls per minute to a telephone switchboard follow a Poisson distribution of λ = 2. Calculate the probabilities that in a given minute. . .1. . . .no calls occur;2. . . .no more than two calls
The company Compsolutions has 40 employees. Of these, 20% are members of the union and would support a strike in the coming labour dispute. Mr. Schaffig’s marketing department consists of six
In the accounting department of the same company, an accountant completes 500 accounting entries per day. The probability of making a mistake is 0.004. What is the probability that the accountant
Researchers count vehicles at two points of an intersection. The number of vehicles that pass by per minute has a Poisson distribution of λ1 = 1.2 and λ2 = 0.8. What is the probability that within
The company Hedonic has made coffee dispensers available to its workers. The coffee consumption of its 100 employees has a normal distribution with an expected value of 130 l/week and a standard
The average weight of chicks the same age and variety is 105 g with a standard deviation of 2.5 g and a normal distribution.1. What is the probability that the weight of a chick is less than 100 g?2.
A machine fills bags of coffee in such a way that the weight of a filled bag has a normal distribution of μ = 510 g and σ = 20 g. The packages are labelled “Net weight: 500 g”.1. What per cent
The company Autotrans specializes in the transport of vehicles between manufacturers and retailers. Every once and a while a car is damaged during transport—a median of 1.21 vehicles per month. The
A storeowner wants to get rid of 25 fireworks from last year in the coming New Year’s season. The manufacturer guarantees that 60% of the fireworks—in this case, 15 units—will ignite after a
Each day a wholesaler makes deliveries to 50 retailers. The probability that a retailer (independently of the others) will return one of the products is 0.03.(a) What is the probability that exactly
Imagine a factory that produces a certain type of machine.(a) The operators know from experience that the probability of a day passing without an error occurring is 0.9048. Which distribution is
A metal cutter produces metal cuts from a running metal band. The pieces must have a certain length μ, but the cutter is somewhat unreliable. Even when it is set to cut the desired length,
(a) How can we reduce error when using a sample to estimate the parameter of a total population?(b) How can we improve accuracy when using a sample to estimate μ?
More than 10,000 customers shop at your store each day. A sample of customers (n = 20) taken from the total population with a normal distribution results in an empirical variance of S2 = 102
The company Tasty Market wants to find new packaging for its pralines. The management is still unsure about which colour to use. Previously, the pralines were packaged in yellow. Now a blue colour is
A car dealer wants to know with 95% confidence what percentage of the 1500 customers who bought a vehicle from him 5 years ago are still driving it today. In a random sample of 250 customers, it
A defendant awaits the verdict in a courtroom. The judges must decide between pronouncing him guilty or not guilty.(a) What are the two mistakes the judges could make in coming to their decision?(b)
Thousand purchasers of a new car receive the questionnaire in Fig. 9.47. For the examples below, indicate the scale and a suitable statistical test for the given variables. Are the samples dependent
The management asks you to check whether products before shipping meet the minimum length stipulated by the customer (150 cm) with a 20% probability of error. After adjusting the machine anew, you
For the examples below, indicate the scale and suitable statistical test for the given variables. Are the samples dependent or independent? If no scale is given, the highest possible scale is
You are investigating the effect of three different advertising strategies (circulars, local newspaper ads, and billboards) on customer preference for a certain product. You measure customer
A study records the overall preference for a product (“How would you rate this product?”) and attitudes towards the price of a product (“It is a fair price”). The result is the crosstab in
The management asks you to say with 99% certainty that the change from yellow to blue packaging will lead to better sales. The yellow packaging led to weekly sales of 10,000 packages on average. The
You are a sales manager for a consumer product and want to maximize the number of individuals in your target customer group, so you decide to run a television commercial. For four channels and three
Figure 9.50 shows the results of a study about the annual revenue from different household types in a supermarket chain. What was studied and how are the results to be interpreted? Household
You are given the task of carrying out a competition analysis for baby food. You ask 120 parents to rate on a scale from one to five how natural they find products from two manufacturers, hupp and
For the buyers of two vehicle brands, you increase the strength of the motors in classified form. This results in the following contingency table:(a) Indicate the expected frequencies in the case of
In an experiment on the effectiveness of music on the willingness of customers to spend money in a supermarket, researchers selected 400 customers at random. Some of the customers shopped on days
After speaking with grocery store customers, you identify household size and the number of purchased bananas and place them in the following contingency table.(a) Identify the empirical chi-square
What was tested in the procedure represented in Fig. 9.54? Interpret the results. Age Age t -2.490 N df 499 500 One-Sample Statistics Mean Std. Deviation 52.8780 One-Sample Test Sig.
You are a manager of an international chain of hardware stores with locations in Germany, France, Spain, and the UK. So far the chain has gone by a different name in each country. Now you want to
You’re an employee in the market research department of a coffee roasting company who is given the job of identifying the euro price of the company’s coffee in various markets and the associated
You’re given the job of identifying the market share of a product in various markets. You determine the market share ranges between 51.28% and 61.08%. You try to estimate the factors influencing
You’re an employee in the market research department of a company that manufactures oral hygiene products. You’re given the task of determining weekly sales of the toothpaste Senso White at a
Shnutella, an international manufacturer of the hazelnut chocolate spread, is looking for a new advertising ambassador and a new product slogan. Because the pan-European football tournament (UEFA
The fast-food chain Burger Slim wants to introduce a new children’s meal. The company decides to test different meals at its 2261 franchises for their effect on total revenue. Each meal variation
The share of the population living in urban areas and infant deaths per 1000 births was collected for 28 European countries. Afterwards the data underwent a hierarchical cluster analysis. The results
The following table presents price and sales trends for consumer goods A, B, C, and D in years 1 and 3.(a) Calculate the Laspeyres price and quantity indices for reporting year 3 using base year 1.
A market research institute studied the relationship between income and personal satisfaction. They used hierarchical clustering to analyse their data.(a) Assume you decide for a four-cluster
Interpret the results of the following factor analysis about university students. KMO and Bartlett's test Kaiser-Meyer-Olkin measure of sampling adequacy Bartlett's test of sphericity Approx.
Each day, more than 10,000 customers shop at a business. A sample with a size of n = 100 from location A has an average customer stay of 45 min. The actual duration has a normal distribution with an