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statistics alive

Questions and Answers of Statistics Alive

If a correlation between two nominal variables is analyzed the phi coefficient or the contingency coefficient should be used.
6.1 Which correlation coefficient should be used for which scales?
6.2 Why are theoretical considerations necessary before calculating a correlation between variables?
6.3 Why does a correlation coefficient say nothing about causality?
6.4 Consider the following three scatterplots, which were discussed by Anscombe nearly fifty years ago in the year 1973. In which of the cases can the Bravais–Pearson correlation coefficient be
6.5 Draw and calculate by hand the scatterplot and the correlation coefficient for the variable growth and marketing for the first eight companies of our data set data_growth.xlsx and interpret the
6.6 Use Excel to draw the scatterplot and to calculate the correlation coefficient of Bravais–Pearson for the variables growth and marketing, growth and innovation, growth and experience, and
6.7 Calculate by hand the rank correlation coefficient of Spearman for the variables growth rate and self-assessment and interpret the result, use the first ten companies in the data set
6.8 Use Excel to calculate the rank correlation coefficient of Spearman for the variables growth and self-assessment and interpret the result. The data set is data_growth.xlsx.
6.9 Calculate the phi coefficient for the variables sex and sector and interpret the result, data set data_growth.xlsx.
6.10 For our data set data_growth.xlsx, calculate the contingency coefficient for the variables sex and motive and interpret the result.
6.11 We are interested in the relationship between CO2 emissions per capita and the gross domestic product per capita in the European Union. In the database of
6.12 We are interested in whether there is a correlation between three stocks. We once again go to the Internet, visit a financial platform (this time perhaps https://www.boerse-online.de/) and
Focus Problem: Fireflies Suppose you are conducting a study to compare firefly populations exposed to normal daylight/darkness conditions with firefly populations exposed to continuous light (24
Census: Web Site Census and You, a publication of the Census Bureau, indicates that “Wherever your Web journey ends up, it should start at the Census Bureau’s site.” Find the Census Bureau’s
Student Life: Data Collection Project Make a statistical profile of your own statistics class. Items of interest might be(a) Height, age, gender, pulse, number of siblings, marital status(b) Number
General: Experiment How would you use a completely randomized experiment in each of the following settings? Is a placebo being used or not? Be specific and give details.(a) A charitable nonprofit
General: Gathering Data Which technique for gathering data (observational study or experiment) do you think was used in the following studies? Explain.(a) The U.S. Census Bureau tracks population
General: Type of Sampling Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience) used in each of the following situations.(a) To conduct a preelection
Simulation: Identity Theft The U.S. Department of Justice examined all reported cases of identity theft for U.S. residents aged 16 or older. Their data show that of all the reported incidents of
Radio Talk Show: Sample Bias A radio talk show host asked listeners to respond either yes or no to the question, “Is the candidate who spends the most on a campaign the most likely to win?”
Statistical Literacy You are conducting a study of students doing work-study jobs on your campus.Among the questions on the survey instrument are:A. How many hours are you scheduled to work each
Critical Thinking Alisha wants to do a statistical study to determine how long it takes people to complete a Sudoku puzzle (see Problem 1 for a description of the puzzle). Alisha’s plan is as
Critical Thinking Sudoku is a puzzle consisting of squares arranged in 9 rows and 9 columns. The 81 squares are further divided into nine 3 3 3 square boxes. The object is to fill in the squares with
Surveys: Manipulation The New York Times did a special report on polling that was carried in papers across the nation. The article pointed out how readily the results of a survey can be manipulated.
General: Completely Randomized Experiment How would you use a completely randomized experiment in each of the following settings? Is a placebo being used or not? Be specific and give details.(a) A
General: Gathering Data Which technique for gathering data (sampling, experiment, simulation, or census) do you think was used in the following studies?(a) An analysis of a sample of 17,000
Ecology: Gathering Data Which technique for gathering data (observational study or experiment) do you think was used in the following studies?(a) The Colorado Division of Wildlife netted and released
Interpretation Suppose you are looking at the 2006 results of how the Echo generation classified specified items as either luxuries or necessities. Do you expect the results to reflect how the Echo
Interpretation Zane is examining two studies involving how different generations classify specified items as either luxuries or necessities. In the first study, the Echo generation is defined to be
Critical Thinking A randomized block design was used to study the amount of grants awarded to students at a large university. One block consisted of undergraduate students and the other block
Critical Thinking A brief survey regarding opinions about recycling was carefully designed so that the wording of the questions would not influence the responses. Charlie administered the survey at a
Statistical Literacy Consider a completely randomized experiment in which a control group is given a placebo for congestion relief and a treatment group is given a new drug for congestion
Statistical Literacy A study of college graduates involves three variables: income level, job satisfaction, and one-way commute times to work. List some ways the variables might be
Discuss potential pitfalls that might make your data unreliable.AppendixLO1
Identify control groups, placebo effects, completely randomized experiments, and randomized block experiments.AppendixLO1
Describe simulations, observational studies, and experiments.AppendixLO1
Define a census.AppendixLO1
Sampling Methods: Health Care Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction
Sampling Methods: Benefits Package An important part of employee compensation is a benefits package, which might include health insurance, life insurance, child care, vacation days, retirement plan,
Education: Test Construction Professor Gill uses true–false questions. She wishes to place 20 such questions on the next test. To decide whether to place a true statement or a false statement in
Education: Test Construction Professor Gill is designing a multiple-choice test. There are to be 10 questions. Each question is to have five choices for answers. The choices are to be designated by
Simulation: Birthday Problem Suppose there are 30 people at a party. Do you think any two share the same birthday? Let’s use the random-number table to simulate the birthdays of the 30 people at
Computer Simulation: Roll of a Die A die is a cube with dots on each face. The faces have 1, 2, 3, 4, 5, or 6 dots. The table below is a computer simulation (from the software package Minitab) of the
Simulation: Coin Toss Use a random-number table to simulate the outcomes of tossing a quarter 25 times.Assume that the quarter is balanced (i.e., fair).AppendixLO1
Sampling: Random Use a random-number table to generate a list of six random numbers from 1 to 8615.Explain your work.AppendixLO1
Sampling: Random Use a random-number table to generate a list of eight random numbers from 1 to 976. Explain your work.AppendixLO1
Sampling: Random Use a random-number table to generate a list of 10 random numbers between 1 and 99.Explain your work.AppendixLO1
Critical Thinking In each of the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been
Critical Thinking Suppose you are assigned the number 1, and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. Explain
Critical Thinking Consider the students in your statistics class as the population and suppose they are seated in four rows of 10 students each. To select a sample, you toss a coin. If it comes up
Critical Thinking Parker took a random sample of size 100 from the population of current season ticket holders to State College men’s basketball games. Then Parker took a random sample of size 100
Interpretation A campus performance series features plays, music groups, dance troops, and stand-up comedy. The committee responsible for selecting the performance groups include three students
Interpretation In a random sample of 50 students from a large university, all the students were between 18 and 20 years old. Can we conclude that the entire population of students at the university
Statistical Literacy A random sample of students who use the college recreation center were asked if they approved increasing student fees for all students in order to add a climbing wall to the
Statistical Literacy Perry conducted a study of the cost of breakfast cereal. They recorded the costs of several boxes of cereal. However, Perry neglected to take into account the number of servings
Statistical Literacy Explain the difference between a simple random sample and a systematic sample.AppendixLO1
Statistical Literacy Explain the difference between a stratified sample and a cluster sample.AppendixLO1
Describe stratified sampling, cluster sampling, systematic sampling, multistage sampling, and convenience sampling.AppendixLO1
Simulate a random process.AppendixLO1
Construct a simple random sample using random numbers.AppendixLO1
Explain the importance of random samples.AppendixLO1
Critical Thinking You are interested in the weights of backpacks students carry to class and decide to conduct a study using the backpacks carried by 30 students.(a) Give some instructions for
Education: Teacher Evaluation If you were going to apply statistical methods to analyze teacher evaluations, which question form, A or B, would be better?Form A: In your own words, tell how this
Fishing: Levels of Measurement Categorize these measurements associated with fishing according to level: nominal, ordinal, interval, or ratio.(a) Species of fish caught: perch, bass, pike, trout(b)
Business: Levels of Measurement Categorize these measurements associated with a robotics company according to level: nominal, ordinal, interval, or ratio.(a) Salesperson’s performance: below
Student Life: Levels of Measurement Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio.(a) Length of time to complete an exam(b) Time
Archaeology: Ireland The archaeological site of Tara is more than 4000 years old. Tradition states that Tara was the seat of the high kings of Ireland.Because of its archaeological importance, Tara
Ecology: Wetlands Government agencies carefully monitor water quality and its effect on wetlands(Reference: Environmental Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is
Advertising: Auto Mileage What is the average miles per gallon (mpg) for all new hybrid small cars? Using Consumer Reports, a random sample of such vehicles gave an average of 35.7 mpg.(a) Identify
Marketing: Fast Food A national survey asked 1261 U.S. adult fast-food customers which meal (breakfast, lunch, dinner, snack) they ordered.(a) Identify the variable.(b) Is the variable quantitative
Interpretation Lucy conducted a survey asking some of her friends to specify their favorite type of TV entertainment from the following list of choices:sitcom; reality; documentary; drama; cartoon;
Critical Thinking Numbers are often assigned to data that are categorical in nature.(a) Consider these number assignments for category items describing electronic ways of expressing personal
Statistical Literacy For a set population, does a parameter ever change? If there are three different samples of the same size from a set population, is it possible to get three different values for
Statistical Literacy What is the difference between a parameter and a statistic?AppendixLO1
Statistical Literacy Are data at the nominal level of measurement quantitative or qualitative?AppendixLO1
Statistical Literacy In a statistical study what is the difference between an individual and a variable?AppendixLO1
How can you design ways to collect data?AppendixLO1
What are other sampling techniques?AppendixLO1
How can you draw a random sample?AppendixLO1
What is the nature of data?AppendixLO1
Why is statistics important?AppendixLO1
What Is Statistics?AppendixLO1
1.1 Describe the sample space of the experiment consisting of flipping four coins simultaneously. Assign the probability to the event consisting of “two heads up and two tails up.” In this
1.2 An experiment consists of rolling two dice simultaneously and independently of one another. Find the probability of the event consisting of having either an odd number in the first roll or a
1.3 In the roll of a die, find the probability of the event consisting of having either an even number or a number greater than 4.
1.4 An experiment consists of rolling two dice simultaneously and independently of one another. Show that the two events, “the sum of the two rolls is 8” and “the first roll shows 5” are not
1.5 An experiment consists of rolling two dice simultaneously and independently of one another. Show that the two events, “first roll is even” and “second roll is even” are statistically
1.6 A box contains 5 balls, of which 3 are red and 2 are blue. Calculate (a) the probability of drawing two consecutive red balls and (b) the probability of drawing two consecutive red balls, given
1.7 A box contains 10 balls that can be either red or blue. Of the first three draws, done with replacement, two result in the draw of a red ball. Calculate the ratio of the probability that there
1.8 In the game of baseball a player at bat either reaches base or is retired. Consider three baseball players: player A was at bat 200 times and reached base 0.310 of times; player B was at bat 250
1.9 An experiment consists of rolling two dice simultaneously and independently of one another. Calculate (a) the probability of the first roll being a 1, given that the sum of both rolls was 5, (b)
2.1 Consider the exponential distribution f .x/ D ex where 0 and x 0. Show that the distribution is properly normalized, and calculate the mean, variance and cumulative distribution F.x/.
2.2 Consider the sample mean as a random variable defined by x D 1N NX iD1 xi (2.23)where xi are identical independent random variables with mean and variance 2.Show that the variance of x is
2.3 J.J. Thomson’s experiment aimed at the measurement of the ratio between the mass and charge of the electron is presented on page 23. Using the datasets for Tube 1 and Tube 2 separately,
2.4 Using J.J. Thomson’s experiment (page 23), verify the statement that “It will be seen from these tables that the value of m=e is independent of the nature of the gas” used in the
2.5 Calculate the sample covariance and correlation coefficient for the following set of data: .0; 2/; .2; 5/; .1; 4/; .3; 1/.
2.6 Prove that the following relationship holds, Var.X/ D EOEX2 2 where is the mean of the random variable X.
3.1 Consider the Gaussian distribution f .x/ D 1p2 2 e.x/2 22 :Calculate the mean and variance and show that all odd moments EOE.X /n of order n 3 are zero.
3.2 Assume that scores from an I.Q. test follow a Gaussian distribution, and that the scores are standardized in such a way that the mean is D 100, and the standard deviation is D 15.(a)

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