Exam 1 Business Statistics
What type of measurement is influenced by outliers?
Mean
What is interval data and examples of it?
Meaningful differences No true zero point. Calendar year (2009, 2010)
What is Ratio data?
Meaningful differences True zero point Income ($48,000, $0)
The median is defined as what?
Middle point in a data set
What measure of central tendency do you use for qualitative data?
Mode
During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period
Must be Positive
What type of data falls under Qualitative data?
Nominal and Ordinal
Frequency distributions are used to describe what types of data?
Nominal, ordinal, interval, and ratio data. All types of data
The covariance between the returns on two assets is negative. This occurs when
On average, the return on one asset increases while the return on the other asset decreases
Differences between data are meaningless with what type of data?
Ordinal
What is the multiplication rule for two independent events?
P(A∩B) = P(B)P(A)
What is the multiplication rule for dependent events?
P(A∩B)/P(B) or P(A∩ B) = P(B)P(A|B)
What are the two sources of data?
Primary and Secondary
What is Ordinal Data and some examples of it?
Ranking allowed No measurable meaning to the number differences. Education level
Describe Scatter plots
Scatter plots provide a picture of the relationship between two data points that are paired together The dependent variable, which is placed on the vertical axis of the scatter plot, is influenced by changes in the independent variable, which is placed on the horizontal axis A trendline provides an approximation of the relationship
What is a frequency distribution?
Shows the number of data observations that fall into a specific interval
Data that describes a characteristic about a sample is known as what?
Statistic
What is conditional probability?
The probability of an event given or knowing that another event has occurred
What is an observation?
The set of measurements obtained for a particular element
What is time series data?
Time series data refers to data collected by recording a characteristic of a subject over several time periods.
Which of the following indicates the strongest relationship between two variables? r = 0.09 r = 2 r = 0.5 r=-0.6
-.06
The covariance between the returns of stocks A and B is -0.112. The standard deviation of the rates of return is 0.26 for stock A and 0.81 for stock B. The correlation of the rates of return between A and B is the closest to
-0.53
What are the characteristics of a Binomial distribution
1. The experiment consists of a fixed number of (Bernoulli) trials, denoted by n 2. Each trial has only two possible outcomes, a success or a failure 3. The probability of a success p and the probability of a failure q are constant throughout the experiment 4. Each trial is independent of the other trials in the experiment
Suppose the dealer incentive per vehicle for Honda's Acura brand is thought to be bell-shaped and symmetrical with a mean of $2,500 and a standard deviation of $300. Based on this information, what interval of dealer incentives would we expect approximately 99.7% of vehicles to fall within?
1600 to 3400
What is the function to find binomial probabilities?
=BINOM.DIST(X,N,P,cumulative)
What is the relative frequency function?
={frequency(search cells, bin array)}
If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true? A. the data set is a sample B. the data set could be either a sample or a population C. the data set includes all subjects of interest in the study D. The data set is a population
A
Which of the following can be represented by a discrete random variable? A. The number of obtained spots when rolling a six-sided die B. The height of college students C. The finishing time of participants in a cross-country meet D. The average outside temperature taken every day for two weeks
A
Which one of the following statements is true for a right-skewed distribution? A. The mean is greater than the median. B. The mean is roughly equal to the median. C. The mean is greater than the mode. D. The mean is less than the median.
A
What is an event?
A collection of outcomes
Which of the following characteristics does the interval scale NOT have? A. There is a true zero point. B. Numerical values are used to measure various characteristics C. Values can be ranked D. The differences between values are valid
A.
Which of the following represents a population and a sample from that population? A. Residents of Albany, New York, and registered voters in Albany, New York B. Fans at a concert who purchase T-shirts, and fans at a concert who purchase soda C. Freshmen at IU and basketball players at IU D. Teachers of a high school and members of the parent-teacher group
A.
Suppose that you conduct a study in which you observe parents and their children interacting at home. You find that the more supportive parents are, the less aggressive their children are. What conclusion can you make?
Level of support and aggression are negatively correlated.
Define a population and what is consists of.
All items of interest in a study and is defined as all members of a specified group under study.
What is Nominal data and some examples of it?
Arbitrary labels for data No ranking allowed. Ex. Eye Color, Zip Codes (19808, 76137)
What is the Law of Large Numbers?
As the number of trails or observations increases, the observed probability of an event (empirical probability) approaches theoretical (classical) probability
Since the population is always larger than the sample, the value of the sample mean A. is always smaller than the true value of the population mean B. could be larger, equal to, or smaller than the true value of the population mean C. is always equal to the true value of the population mean D. is always larger than the true value of the population mean
B
The data represents the stock price for Google at the end of the past four quarters. Which of the following types of data best describes these values? A. Cross-sectional B. Time series C. Nominal D. Ordinal
B
How do you find the median if the number of observations in a data set is odd? What about even?
By taking the middle value in the sorted data set. The average value of the two middle items when all items are arranged in ascending order.
The Boom company has recently decided to raise the salaries of all employees by 10%. Which of the following is(are) expected to be affected by this raise? A. Mean and mode only B. Mean and median only C. Mean, median, and mode D. Mode and Median only
C
A recent survey of 200 small firms (annual revenue less than $10 million) asked whether an increase in the minimum wage would cause the firm to decrease capital spending. Possible responses to the survey question were: "Yes," "No," or "Don't Know." The scale of measurement for the data generated by this survey question is best classified as A. ordinal B. interval C. nominal D. ratio
C.
The standard deviation of a sample of 100 elements taken from a very large population is determined to be 60. The variance of the population
Can be any value greater or equal to zero
What is qualitative data and some examples?
Classified by descriptive terms (labels or names used to identify an attribute of elements) Examples: • Marital Status • Political Party • Eye Color (Defined categories)
Comparing the consistency (variability) between two data sets when their means are very different is best done with the
Coefficient of variation
What is Descriptive statistics?
Collecting, summarizing, and displaying data (reported based on observations)
A numerical measure of linear association between two variables is the
Correlation coefficient
What measures the direction of the linear relationship between two variables but does not measure the strength of the relationship?
Covariance
What is cross sectional data?
Cross-sectional data refers to data collected by recording a characteristic of many subjects at the same point in time, or without regard to differences in time.
What is Quantitative Data and its types?
Described by numerical values (how many or how much) 1. Counted Examples: Number of Children Defects per hour (Counted items) 2. Measured Examples: • Weight • V oltage (Measured characteristics)
What is the expected value for discrete probability distribution? define the variables
E(x) = μ = ∑x P(x ) μ = The mean of the discrete probability distribution xi = The value of the random variable for the ith outcome P(xi) = The probability that the ith outcome will occur n = The number of outcomes in the distribution
Why do we calculate inferential statistics?
Estimate unknown population parameters
How do you estimate class width and define the variables
Estimated class width=(Maximum data value-min data value)/k. k=number of classes The width is the range of numbers to put into each class • Round this estimate to a useful whole number that makes the frequency distribution more readable
Which of the following variables is qualitative? A. Gender B. Values corresponding to a qualitative variable are typically expressed in words. C. Height D. Temperature E. Weight
Gender
What are some examples of quantitative variables?
House size, house price, house age, numbers
What type of data falls under Quantitative data?
Interval and Ratio
What scales of data measurement are associated with quantitative data?
Interval and ratio
The Fahrenheit scale for measuring temperature would be a(n)
Interval scale
Is it possible for a data set to have more than one mode?
Yes, if two or more values in a data set occur with the most frequency
What is true concerning the attributes of z-scores?
Z-scores are negative for data values below the mean of the distribution. Z-scores are equal to zero for data values equal to the mean of the distribution. Z-scores are positive for data values above the mean of the distribution.
What is a variable?
a characteristic of interest for the elements
What is a Parameter?
a described characteristic about a population
What is a statistic?
a described characteristic about a sample
What is probability and how is it measured?
a numerical measure of the likelihood that an event will occur Probability values are always assigned on a scale from 0 to 1.
Positive values of the correlation indicate
a positive relation between the independent and the dependent variables
What is a sample space?
an experiment is the set of all experimental outcomes
What is an experiment?
any process that generates well- defined outcomes
What is discrete data and what are some examples of it?
are values based on observations that can be counted and are typically represented by whole numbers (how many) • something that has been counted • take on whole numbers such as 0, 1, 2, 3 Examples: • Number of children per family • Number of cars listed per insurance policy • Vacation days per month
What is continuous data and some examples of it?
are values that can take on any real numbers, including numbers that contain decimal points (how much) • usually measured rather than counted Examples: • Time required to read chapter 2 • Thickness of paint applied to a car body • Person's height
Why are population parameters difficult to calculate?
both cost prohibitions on data collection and the infeasibility of collecting data on the entire population. Gathering population data can be very expensive and difficult if not impossible to obtain.
What is the binomial probability distribution function?
calculates the probability of a specific number of successes (x) for a certain number of trials (n), given specified probability of success (p) and probability of failure (q) P(x,n) = ((n!)/(n−x))*p^x*q^n-x P(x,n)=The probability of observing x successes in n trials n = Number of trials x = Number of successes p = Probability of a success q = Probability of a failure
Which symbol represents the standard deviation of the population?
curly cursive o
What is secondary data, advantages and disadvantages?
data collected by someone else. Advantages: Readily available Less expensive to collect Disadvantages: No control over how the data was collected Less reliable unless collected and recorded accurately
Define Information
data that are transformed into useful facts that can be used for a specific purpose, such as making a decision ... it is more than just data
What is Primary data, its collection methods, advantages and disadvantages?
data that you have collected for your own use. Collection Methods: Direct Observations Experiments Surveys Advantages: Collected by the person or organization who uses the data Disadvantages: Can be expensive and time-consuming to gather
Your business statistics class had a test last week. The average score for the class is an example of what?
descriptive statistics
What is Relative Frequency distribution?
display the proportion of observations in each class relative to the total number of observations • shows the fraction of observations in each class • found by dividing each frequency by the total number of observations • the fractions in a relative frequency distribution add up to 1.00
What is mutually exclusive?
if events have no outcomes in common
What is an independent event?
if the occurrence of one event has no impact on the occurrence of the other event
What is a histogram?
is a graph showing the number of observations in each class of a frequency distribution or the relative frequency of the class: 1. The variable of interest is placed on the horizontal axis 2. A rectangle is drawn above each class interval with its height corresponding to the frequency or relative frequency
What is a random variable?
is a numerical description of the outcome of an experiment
What is the mean of a discrete probability function and its symbol?
is the weighted average of ALL values of the random variable. • The weights are the probabilities • The mean does not have to be a value the random variable can assume
What is Inferential statistics?
making claims or conclusions about the data based on a sample (makes statement about population)
What is a continuous random variable?
may assume any numerical value in an interval or collection of intervals •Oftenmeasured,fractionalvaluesarepossible • timerequiredtocompleteatask;height,ininches
What is a discrete random variable?
may assume either a finite number of values or an infinite sequence of values • Values are whole numbers (integers), usually counted number of complaints per day; number of TVs in a household
What is the mean and Standard Deviation of a Binomial Distribution?
mean= μ = np Standard Deviation= σ= SQRT(npq) μ = The mean of the binomial distribution σ = The standard deviation of the binomial distribution n = The number of trials p = The probability of a success q = The probability of a failure
The covariance ranges between
minus infinity and plus infinity
u is an example of a
population paramater
What is the scale of measurement of the distance between any location?
ratio
What are class boundaries?
represent the minimum and maximum values for each class
What is an element?
the entities on which data are collected
Define statistics
the mathematical science that deals with the collection, analysis, and presentation of data, which can then be used as a basis for inference and induction
What is cumulative relative frequency distribution?
totals the proportion of observations that are less than or equal to the class at which you are looking • shows the accumulated proportion as class values vary from low to high • cumulative relative frequency for the highest class is equal to 1.00
What is the multiplication rule and how is it used?
used to determine the probability of the intersection (joint probability) of two events occurring, or P(A and B)
Define data
values assigned to observations or measurements All the data collected in a particular study are referred to as the data set for the study
What is Cross Section Data?
values collected from a number of subjects during a single time period
What is Time Series Data?
values that correspond to specific measurements taken over a range of time periods
Which of the following symbols represents the mean of the sample?
x with line on top
What are some examples of a binomial distribution?
• Flip of a coin: H or T • A survey response to a question is "yes I will buy" or "no I will not" • New job applicants either accept an offer or reject it
What is a discrete probability distribution?
• a listing of all the possible outcomes of an experiment for a discrete random variable • along with the relative frequency of each outcome • describes how probabilities are distributed over the values of the random variable • can be represented by a table, graph, or formula • is defined by a probability function, denoted by P(x) (sometimes f(x)), which provides the probability for each value of the random variable x
When do you use a contingency table?
• one variable is qualitative, another is quantitative • both variables are qualitative • both variables are quantitative
