Accounting
Anthropology
Archaeology
Art History
Banking
Biology & Life Science
Business
Business Communication
Business Development
Business Ethics
Business Law
Chemistry
Communication
Computer Science
Counseling
Criminal Law
Curriculum & Instruction
Design
Earth Science
Economic
Education
Engineering
Finance
History & Theory
Humanities
Human Resource
International Business
Investments & Securities
Journalism
Law
Management
Marketing
Medicine
Medicine & Health Science
Nursing
Philosophy
Physic
Psychology
Real Estate
Science
Social Science
Sociology
Special Education
Speech
Visual Arts
Computer Science
Q:
Two events A and B are said to mutually be exclusive if P(A and B)= 0.
Q:
The temperature of the room in which you are writing this test is a continuous random variable.
Q:
Marginal probability is the probability that a given event will occur, given that another event has already occurred.
Q:
The relative frequency of an event is the number of times the event occurs out of the total number of times the random experiment is run.
Q:
If A and B are two independent events with P(A) = 0.20 and P(B) = 0.60, then P(A and B) = 0.80
Q:
Suppose A and B are mutually exclusive events where P(A) = 0.2 and P(B) = 0.5, then P(A or B) = 0.70.
Q:
Two events are said to be independent when knowledge of one event is of no value when assessing the probability of the other.
Q:
A car dealer collected the following information about a sample of 448 Grand Rapids residents:
Exact salaries of these Grand Rapids residents
Education level (completed high school only or completed college)
Income level (low or high)
Car finance (whether or not the last purchased car was financed)
Using the education level, income level, and car finance data, he created the three pivot tables shown below. Based on these tables; determine how education and income influence the likelihood that a family finances a car.
Q:
What other data would you need to be more confident that increased income inequality leads to lower unemployment?
Q:
Do these data help to confirm or contradict the hypothesis that increased wage inequality leads to lower unemployment levels? [Hint: construct a scatterplot]
Q:
NARRBEGIN: SA_82_84Economists believe that countries with more income inequality have lower unemployment rates. An economist in 1996 developed the Table below which contains the following information for ten countries during the 1980-1995 time period:The change from 1980 to 1995 in ratio of the average wage of the top 10% of all wage earners to the median wageThe change from 1980 to 1995 in unemployment rate.Income inequality vs. Unemployment rateCountryWIR ChangeUR Change Germany-6.0%6.0% France-3.5%5.6% Italy1.0%5.2% Japan0.0%0.6% Australia5.0%2.4% Sweden4.0%5.9% Canada5.5%2.0% New Zealand9.5%4.0% Britain15.6%2.5% U.S.15.8%-1.8% NARRENDExplain why the ratio of the average wage of the top 10% of all wage earners to the median measures income inequality.
Q:
Approximate the percentage of these internet users who are women in the 30-43 age group.
Q:
What percentage of these internet users has formal education beyond high school?
Q:
Approximate the percentage of these internet users who are women.
Q:
Approximate the percentage of these Internet users who are in the 58-71 age group.
Q:
What percentage of these Internet users who are married.
Q:
Approximate the percentage of these Internet users who are married with formal education beyond high school.
Q:
What is the average annual salary of the employed Internet users in this sample?
Q:
NARRBEGIN: SA_72_81
A recent survey data collected from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status and annual income. Using Excel, the following pivot tables were produced. NARREND
Approximate the percentage of these Internet users who are currently employed.
Q:
NARRBEGIN: SA_72_81
A recent survey data collected from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status and annual income. Using Excel, the following pivot tables were produced. NARREND
Approximate the percentage of these Internet users who are single with no formal education beyond high school.
Q:
NARRBEGIN: SA_72_81
A recent survey data collected from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status and annual income. Using Excel, the following pivot tables were produced. NARREND
Approximate the percentage of these Internet users who are men under the age of 30.
Q:
The following scatterplot compares the selling price and the appraised value. Is there a linear relationship between these two variables? If so, how would you characterize the relationship?
Q:
There are two scatterplots shown below. The first chart shows the relationship between the size of the home and the selling price. The second chart examines the relationship between the number of bedrooms in the home and its selling price. Which of these two variables (the size of the home or the number of bedrooms) seems to have the stronger relationship with the home's selling price? Justify your answer.
Q:
The table shown below contains information technology (IT) investment as a percentage of total investment for eight countries during the 1990s. It also contains the average annual percentage change in employment during the 1990s. Explain how these data shed light on the question of whether IT investment creates or costs jobs. (Hint: Use the data to construct a scatterplot)Country% IT% ChangeNetherlands2.5%1.6%Italy4.1%2.2%Germany4.5%2.0%France5.5%1.8%Canada8.3%2.7%Japan8.3%2.7%Britain8.3%3.3%U.S.12.4%3.7%
Q:
A health magazine reported that a man's weight at birth has a significant impact on the chance that the man will suffer a heart attack during his life. A statistician analyzed a data set for a sample of 798 men, and produced the pivot table and histogram shown below. Determine how birth weight influences the chances that a man will have a heart attack.
Q:
Of those in the sample who did well in the final exam, what percentage of them spent the weekend before the exam studying?
Q:
Of those in the sample who went partying the weekend before the final exam, what percentage of them did poorly in the exam?
Q:
If the sample is a good representation of the population, what percentage of those who did poorly on the final exam should we expect to have spent the weekend studying?
Q:
If the sample is a good representation of the population, what percentage of those who spent the weekend studying should we expect to do poorly on the final exam?
Q:
If the sample is a good representation of the population, what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam?
Q:
What percentage of the students in the sample went partying the weekend before the final exam and did poorly on the exam?
Q:
What percentage of the students in the sample spent the weekend studying and did well in the final exam?
Q:
What percentage of the students in the sample went partying the weekend before the final exam and did well in the exam?
Q:
NARRBEGIN: SA_58_67A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result. Did Well in ExamDid Poorly in ExamStudying for Exam6015Went Partying2253NARRENDOf those in the sample who did well on the final exam, what percentage of them went partying the weekend before the exam?
Q:
NARRBEGIN: SA_58_67A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result. Did Well in ExamDid Poorly in ExamStudying for Exam6015Went Partying2253NARRENDOf those in the sample who went partying the weekend before the final exam, what percentage of them did well in the exam?
Q:
A data set from a sample of 399 Michigan families was collected. The characteristics of the data include family size (large or small), number of cars owned by family (1, 2, 3, or 4), and whether family owns a foreign car. Excel produced the pivot table shown below. Use this pivot table to determine how family size and number of cars owned influence the likelihood that a family owns a foreign car.
Q:
A sample of 30 schools produced the pivot table shown below for the average percentage of students graduating from high school. Use this table to determine how the type of school (public or Catholic) that students attend affects their chance of graduating from high school.
Q:
The students at small community college in Iowa apply to study either English or Business. Some administrators at the college are concerned that women are being discriminated against in being allowed admittance, particularly in the business program. Below, you will find two pivot tables that show the percentage of students admitted by gender to the English program and the Business school. The data has also been presented graphically. What do the data and graphs indicate? English programGender No YesTotalFemale46.0%54.0%100%Male60.8%39.2%100%Total53.5%46.5%100% Business schoolGender No YesTotalFemale69.2%30.8%100%Male64.1%35.9%100%Total65.4%34.6%100%
Q:
Three samples, regarding the ages of teachers, are selected randomly as shown below:
Sample A: 17 22 20 18 23
Sample B: 30 28 35 40 25
Sample C: 44 39 54 21 52
How is the value of the correlation coefficient r affected in each of the following cases?
a) Each X value is multiplied by 4.
b) Each X value is switched with the corresponding Y value.
c) Each X value is increased by 2.
Q:
NARRBEGIN: SA_51_53
An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household.
The correlation for each pairing of variables are shown in the table below:
Table of correlations NARREND
Which of the variables have essentially no linear relationship with the household's average monthly expenditure on utilities?
Q:
NARRBEGIN: SA_51_53
An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household.
The correlation for each pairing of variables are shown in the table below:
Table of correlations NARREND
Which of the variables have a negative linear relationship with the household's average monthly expenditure on utilities?
Q:
NARRBEGIN: SA_51_53
An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household.
The correlation for each pairing of variables are shown in the table below:
Table of correlations NARREND
Which of the variables have a positive linear relationship with the household's average monthly expenditure on utilities?
Q:
The percentage of the US population without health insurance coverage for samples from the 50 states and District of Columbia for both 2003 and 2004 produced the following table of correlations.Table of Correlations:Percent 20031.000 Percent 2003 Percent 2004Percent 20040.9031.000What does the table for the two given sets of percentages tell you in this case?
Q:
How would you characterize the relationship between gender and annual salary?
Q:
NARRBEGIN: SA_47_49Below you will find current annual salary data and related information for 30 employees at Gamma Technologies, Inc. These data include each selected employees gender (1 for female; 0 for male), age, number of years of relevant work experience prior to employment at Gamma, number of years of employment at Gamma, the number of years of post-secondary education, and annual salary. The tables of correlations and covariances are presented below.Table of CorrelationsGender Age Prior Exp Gamma ExpEducationSalaryGender1.000Age-0.1111.000Prior Exp0.0540.8001.000Gamma Exp-0.2030.9160.5871.000Education-0.0390.5180.4340.3421.000Salary-0.1540.9230.7230.8700.6171.000Table of Covariances (variances on the diagonal)GenderAgePrior ExpGamma ExpEducationSalaryGender 0.259Age-0.633 134.051Prior Exp 0.117 39.060 19.045Gamma Exp-0.700 72.047 17.413 49.421Education-0.033 9.951 3.140 3.987 2.947Salary-1825.97249702.3573699.75143033.2924747.68584640062NARRENDFor which of the two variables, number of years of prior work experience or number of years of post-secondary education, is the relationship with salary stronger? Justify your answer.
Q:
NARRBEGIN: SA_47_49Below you will find current annual salary data and related information for 30 employees at Gamma Technologies, Inc. These data include each selected employees gender (1 for female; 0 for male), age, number of years of relevant work experience prior to employment at Gamma, number of years of employment at Gamma, the number of years of post-secondary education, and annual salary. The tables of correlations and covariances are presented below.Table of Correlations Gender Age Prior Exp Gamma ExpEducationSalaryGender1.000 Age-0.1111.000 Prior Exp0.0540.8001.000 Gamma Exp-0.2030.9160.5871.000 Education-0.0390.5180.4340.3421.000 Salary-0.1540.9230.7230.8700.6171.000Table of Covariances (variances on the diagonal) GenderAgePrior ExpGamma ExpEducationSalaryGender 0.259 Age-0.633 134.051 Prior Exp 0.117 39.060 19.045 Gamma Exp-0.700 72.047 17.413 49.421 Education-0.033 9.951 3.140 3.987 2.947 Salary-1825.97249702.3573699.75143033.2924747.68584640062NARRENDWhich two variables have the strongest linear relationship with annual salary?
Q:
If we draw a straight line through the points in a scatterplot and most of the points fall close to the line, there is a strong positive linear relationship between the two variables.
Q:
Statisticians often refer to the pivot tables as contingency tables or crosstabs.
Q:
The scatterplot is a graphical technique used to describe the relationship between two numerical variables.
Q:
If the standard deviation of X is 15, the covariance of X and Y is 94.5, the coefficient of correlation r = 0.90, then the variance of Y is 7.0.
Q:
The advantage that the coefficient of correlation has over the covariance is that the former has a set lower and upper limit.
Q:
If the coefficient of correlation r = 0 .80, the standard deviations of X and Y are 20 and 25, respectively, then Cov(X, Y) must be 400.
Q:
It is possible that the data points are close to a curve and have a correlation close to 0, because correlation is relevant only for measuring linear relationships.
Q:
If the standard deviations of X and Y are 15.5 and 10.8, respectively, and the covariance of X and Y is 128.8, then the coefficient of correlation r is approximately 0.77.
Q:
The correlation between two variables is a unitless and is always between "1 and +1.
Q:
Generally speaking, if two variables are unrelated, the covariance will be a positive or negative number close to zero
Q:
The cutoff for defining a large correlation is >0.7 or <-0.7.
Q:
We do not even try to interpret correlations numerically except possibly to check whether they are positive or negative
Q:
Correlation is a single-number summary of a scatterplot
Q:
Correlation has the advantage of being in the same original units as the X and Y variables
Q:
To form a scatterplot of X versus Y, X and Y must be paired
Q:
A trend line on a scatterplot is a line or a curve that fits the scatter as well as possible
Q:
Correlation and covariance can be used to examine relationships between numerical variables and categorical variables that have been coded numerically.
Q:
We must specify appropriate bins for side-by-side histograms in order to make fair comparisons of distributions by category.
Q:
Side-by-side boxplots allow you to quickly see how two or more categories of a numerical variable compare
Q:
Problems in data analysis where we want to compare a numerical variable across two or more subpopulations are called comparison problems.
Q:
Joint categories for categorical variables cannot be used to make inferences about the relationship between the individual categorical variables.
Q:
An example of a joint category of two variables is the count of all non-drinkers who are also nonsmokers.
Q:
Counts for categorical variable are often expressed as percentages of the total.
Q:
Which of the following are true statements of pivot tables?
a. They allow us to "slice and dice" data in a variety of ways.
b. Statisticians often refer to them as contingency tables or crosstabs.
c. Pivot tables can list counts, averages, sums, and other summary measures, whereas contingency tables list only counts.
d. All of these options
Q:
Which of the following statements are false?
a. Contingency tables are traditional statistical terms for pivot tables that list counts.
b. Time series plot is a chart showing behavior over time of a time series variable.
c. Pivot table is a table in Excel that summarizes data broken down by one or more numerical variables.
d. None of these options
Q:
The tables that result from pivot tables are called:
a. samples
b. sub-tables
c. specimens
d. crosstabs
Q:
The tool that provides useful information about a data set by breaking it down into subpopulations is the:
a. histogram
b. scatterplot
c. pivot table
d. spreadsheet
Q:
A scatterplot allows one to see:
a. whether there is any relationship between two variables
b. what type of relationship there is between two variables
c. Both options are correct
d. Neither option is correct
Q:
If Cov(X,Y) = - 16.0, variance of X = 25, variance of Y = 16 then the sample coefficient of correlation r is
a. + 1.60
b. " 1.60
c. " 0.80
d. + 0.80
e. Cannot be determined from the given information
Q:
A perfect straight line sloping downward would produce a correlation coefficient equal to
a. +1
b. "1
c. 0
d. +2
e. "2
Q:
Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be
a. a large positive number
b. a large negative number
c. a positive or negative number close to zero
d. a positive or negative number close to +1 or -1
Q:
Which of the following are considered measures of association?
a. Mean and variance
b. Variance and correlation
c. Correlation and covariance
d. Covariance and variance
e. First quartile and third quartile
Q:
The correlation is best interpreted
a. By itself
b. Along with the covariance
c. Along with the corresponding scatterplot
d. Along with the corresponding contingency chart
e. Along with the mean and standard deviation
Q:
We are usually on the lookout for large correlations near
a. +1
b. -1
c. Either of these options
d. Neither of these options