statistics stoof
A polygon uses
uses a continuous line to represent the shape of the distribution of a data set.
A numerical value that measures the likelihood of an uncertain event is a ______.
probability
If A and B are independent events, then
P(A) = P(A|B)
Which of the following is an example of quantitative data?
Facebook's closing stock price today
Which of the following graphical depictions allows you to examine the relationship between two variables?
Scatter plot
Which of the following statements about the mean absolute deviation (MAD) is MOST accurate?
MAD is expressed in the same units as the original data.
Which of the following is true about relative frequency and cumulative relative frequency distributions? Select all that apply.
The sum of the relative frequencies is 1. The cumulative relative frequency for the last class is always 1.
The range is the difference between
the largest and the smallest values.
For all normally distributed random variables, the
the mean, the median, and the mode are all equal.
The median is defined as
the middle value of a data set.
Since the z table provides the cumulative probabilities for a given value of z, what is the P(0 < Z < z)?
the result of subtracting 0.5 from the value found by looking up z in the table.
In a given cumulative frequency distribution, the "cumulative frequency" column value for the third class represents
the sum of observations in the first, second and third classes.
The addition rule is used to calculate
the union of two events.
Since the z table provides the cumulative probabilities for a given value of z, what is the P(Z < z)?
the value found by looking up z in the table.
Two widely used measures of dispersion are
the variance and the standard deviation.
A positive z-score indicates that the sample value is
to the right of the mean.
A knowledge of statistics provides the necessary tools to differentiate between sound statistical conclusions and questionable conclusions drawn from incomplete data points or just misinformation.
true
A population is defined as all members of a specified group.
true
Compared to the nominal scale, the ordinal scale reflects a stronger level of measurement
true
Contingency tables are useful to analyze
two categorical variables.
When a characteristic of interest differs among various observations, then it can be termed a
variable
All of the following are measures of central location EXCEPT the ______.
variance
When calculating the variance and standard deviation for a discrete random variable, the squared differences about the mean are
weighted by the probabilities of each value.
Chebyshev's theorem is applicable
when the data have any shape.
Percentiles for a normally distributed random variable can be found most easily by using which of the following formulas?
x = μ + zσ
Consider data that are normally distributed. In order to transform a value x into it standardized value z, we use the following formula:
z = x−μ/σ
If the P(Z<z) is greater than 0.5, then
z must be positive.
If the P(Z>z) is less than 0.5, then
z must be positive.
The exponential random variable is bounded below by _______.
zero
Probability values range from
zero to one.
Which one of the following z-scores indicates that an observation is an outlier?
|z| > 3
In the following scenarios, indicate those that describe a Poisson random variable.
- The number of leaks in a specified stretch of a pipeline - The number of customers who purchase concessions over the next hour at a movie theater
The probability that a normal random variable X is less than its mean is equal to
.5
The mean and variance of the standard normal distribution are ______, respectively.
0 and 1
For a discrete probability distribution, which best describes the probability of each value x?
0 ≤ P(X = x) ≤ 1
What are the two key properties of a discrete probability distribution?
0 ≤ P(X = x) ≤ 1 and ∑P(X=xi)∑P(X=xi) = 1
Let event Z be an outcome of an experiment. What are possible probabilities for Z? Select all that apply.
0.12 0 1.00
P(Z<0) equals ____. Select all that apply.
0.5 P(Z>0) P(Z≤0)
The sum of the probabilities of all possible x values in a discrete distribution equals what?
1
For any given event, the probability of that event and the probability of the complement of the event must sum to ___.
1.0
For any given event, the probability of that event and the probability of the complement of the event must sum to ___.v
1.0
Suppose that the 12th percentile of starting salaries for accounting graduates from your college is $41,000. What does this mean?
12% of the graduates earn less than $41,000.
Consider the following data set: 4, 4, 5, 6, 9, 9. Find the mode(s).
4 and 9
Pat's time in the 1600-meter run placed Pat in the 85th percentile in the school. What percentage of students are faster than Pat?
85%
The empirical rule states that approximately ______ of observations will fall within two standard deviations of the mean.
95%
Since the z table provides the cumulative probabilities for a given value of z, how can we calculate P(Z > z)?
= 1 - P(Z ≤ z)
With respect to a bar chart, which of the following statements is MOST accurate?
A bar chart is a useful graphical tool for qualitative data.
What assumption is made with classical method of determining probabilities?
All outcomes are equally likely.
The relative frequency of an event is used to calculate what type of probability?
An empirical probability
The owner of BevaMart wants to study the relationship between the outside temperature and hot chocolate sales. The owner found the covariance between the two variables outside to be -81.46. Based on the covariance, which option best describes the linear relationship between temperature and hot chocolate?
As the temperature increases, hot chocolate sales decrease.
Which of the following are examples of a binomial experiment?
Ask 27 customers at a movie theater if they spent $20 or more on concessions. Ask 12 randomly-selected people whether they are members of Facebook.
Which of the following BEST represents an empirical probability?
Based on past data, a manager believes there is a 83% selling out of a particular product today.
When updating a prior probability based on new information, which of the following methodologies is MOST useful?
Bayes' Theorem
Which distribution is appropriate when counting the number of successes in n trials if the probability of success p remains constant from trial to trial?
Binomial
Quantitative variables can be summarized in a contingency table by doing which of the following?
Create categories for the quantitative variables.
Which of the following are true? Select all that apply.
Half the data is below the second quartile. The second quartile equals the median.
Which of the following graphical depictions is useful for observing the spread of the data for a single variable?
Histogram
Suppose there is a jar with 3 red and 3 white marbles in it. If you wanted to know what the probability would be for you to select two marbles randomly (without replacement) and get one marble of each color, what probability distribution would you use?
Hypergeometric
Which distribution provides the most accurate probabilities for the number of successes when we sample without replacement from a population whose size N is not significantly larger than the sample size n?
Hypergeometric since the probability of success p changes noticeably from trial to trial
Which scales of data measurement are associated with quantitative data?
Interval and ratio
Which of the following statements is accurate about a Poisson random variable?
It counts the number of successes in a specified time or space interval.
What does it mean to say that the exponential distribution is "memoryless"?
It has a constant failure rate.
What is the common notation for random variables?
It is common to denote random variables by upper-case letters and particular values of the random variables by the corresponding lower-case letters.
Which scales of data measurement are associated with qualitative data?
Nominal and ordinal
Which of the following are example(s) of quantitative data?
Number of parking tickets sold today miles per gallon lifetime of a lightbulb
Which of the following graphical depictions displays cumulative data?
Ogive
How many outcomes of an experiment constitute a simple event?
One
Which one of the following words is associated with the union of two events?
Or
An undergraduate student's status (freshman, sophomore, junior, or senior) is an example of which scale of measurement?
Ordinal scale
The addition rule for two events A and B is
P(A) + P(B) - P(A∩B)
The complement rule with respect to event A is
P(AC) = 1 - P(A)
For two events A and B, the multiplication rule is
P(A∩B) = P(A|B) × P(B).
A cumulative distribution function explicitly displays
P(X≤x).
Due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to
P(Z < -1.5)
The z table in the text provides the cumulative probability for a given value z. What does "cumulative probability" mean?
P(Z≤z)
Assume the sample space S = {win, lose}. Which numbers define valid probabilities?
P(win) = 0.8, P(lose) = 0.2
When constructing a histogram, what values/labels go on the horizontal (x) axis and the vertical (y) axes?
Quantitative class limits on the horizontal axis; frequency or relative frequency on the vertical axis.
San Francisco 49ers' linebacker Patrick Willis won the Defensive Rookie of the Year Award in 2007 with a total of 174 tackles. Tackles are measured on what kind of a scale? Is a variable measuring the number of tackles considered continuous or discrete?
Ratio scale; discrete
A statistics student interviews for a job. After being asked what her chances of getting the job are, she states that the thinks she has an 80% chance of getting the job. What type of method did she use to determine this probability?
Subjective
Which method(s) can be used to help implement the total probability rule? Select all that apply.
Tabular method. A probability tree
The exponential distribution is related to which distribution?
The Poisson distribution
A researcher wants to compare the variability of two data sets that have different units of measurement. Which of the following measures is MOST useful as a relative measure of dispersion?
The coefficient of variation
All of the following are features of a discrete uniform distribution EXCEPT:
The distribution is bell-shaped.
Which of the following values are included in a box plot? Select all that apply.
The first quartile The median The 75th percentile
Which of the following statements is LEAST accurate?
The height of each rectangle represents cumulative frequency or cumulative relative frequency.
Sometimes the union of two events will be overstated if the union is found by adding just the individual probabilities. What is done to keep from overstating the probability of the union of two events?
The intersection of the event is subtracted.
Which of the following values is NOT part of the 'five-number summary'?
The mean
Mean-variance analysis uses risk and reward to evaluate the rate of return of an asset. How are the risk and reward measured?
The measure associated with risk is the variance, while the measure associated with reward is the mean.
Why is the normal distribution such an important probability distribution?
The normal distribution plays a key role in statistical inference.
Which of the following statements is NOT true?
The number of bankruptcies that are filed in a month is an example of a binomial random variable.
Which of the following can be represented by a discrete random variable?
The number of defective light bulbs in a sample of five bulbs
Which of the following variables is not continuous?
The number of obtained heads when a fair coin is tossed 20 times
Which one of the following is true about ogives?
The only difference in ogives that plot cumulative frequencies and those that plot cumulative relative frequencies is the scale on the y-axis.
When considering the union of two events, A and B, which ones of the following would be included? Select all that apply.
The outcomes that form event A. The outcomes that are in both events A and B. The outcomes that form event B.
Which of the following is true about the formula for finding the 83rd percentile? Select all that apply.
The percentile would be greater than the mean. The z-value would be positive.
Since there are only two outcomes, 'success' and 'failure,' what must be true about their probabilities?
The probabilities must add to one.
Which of the following is an example of a conditional probability?
The probability that Lisa passes the test, given that she attends class and does the homework.
Which of the following are true about the range? Select all that apply.
The range is influenced by extreme values. The range only looks at the two extremes. The range is easy to calculates.
Which one of the following is true?
The standard normal distribution is a special case of the normal distribution.
Which of the following are true about the normal curve? Select all that apply.
The total area under the curve equals 1. The area above the mean equals the area below the mean.
Bayes' theorem is calculated by using what rule in the denominator?
The total probability rule.
Which of the following are true? Select all that apply.
The variance and standard deviation increase as the data becomes more spread out. The variance and standard deviation calculate squared deviations.
Which of the following characteristics does the interval scale not have?
There is a true zero point.
Which of the following are true about bard charts? Select all that apply.
They can display relative frequencies. They can display frequencies. The bars don't touch.
Data of the stock price for Google was collected at the end of the past four quarters. Which of the following types of data best describe these values?
Time series
True or false: Statistical inference is generally based on the assumption of the normal distribution.
True
When two variables exhibit a negative relationship,
Y decreases as X increases.
Which of the following is an example of qualitative data?
Your last name
A discrete random variable X may assume an
a countable number of distinct values.
The coefficient of variation is BEST described as
a relative measure of dispersion.
The expected value of the discrete random variable X is
a weighted average of all possible values of X.
A continuous random variable X follows the uniform distribution with a lower limit of a and an upper limit of b. The expected value of X is calculated as ______.
a+b/2
a. Before flipping a fair coin, Sunil assesses that he has a 50% chance of obtaining tails. b. At the beginning of the semester, John believes he has a 90% chance of receiving straight A's. c. A political reporter announces that there is a 47% chance that the next person to come out of the conference room will be a Republican, since there are 85 Republicans and 96 Democrats in the room.
a. classical b. subjective c. empirical
One of the primary goals when constructing a frequency distribution for quantitative data is to summarize the data in a manner that
accurately depicts the data as a whole.
The purpose of the standard transformation is to
allow for the calculation of probabilities of any normal random variable.
Transforming Normal Random Variables
allows for the z-table to be used for determining probabilities.
A continuous random variable X can assume
an infinite number of values over some interval.
Stem-and-leaf diagrams can be used to (Select all that apply)
analyze the shape of the data. determine how dispersed the data are. observe individual data points.
For a z-value greater than 0, the P(Z<z) will be
between 0.5 and 1.
A contestant on a game show has a choice between taking $1,500 in cash or a prize hidden behind a curtain. The prize behind the curtain could be worth thousands of dollars or nothing. The expected value of the prize behind the curtain is $2,500. If the contestant is risk neutral, then the contestant will
choose the prize because its expected value exceeds the risk-free cash value of $1,500.
A probability based on logical analysis rather than on observation or personal judgment is BEST referred to as a(n):
classical probability.
The inverse transformation, x = μ + zσ is used to ______.
compute x values for given probabilities
A ______ probability is the probability of an event given that another event has already occurred.
conditional
For hotels in New York City, a travel web site wants to provide information comparing hotel costs (high, average, low) versus the quality ranking of the hotel (excellent, good, fair, poor). A useful way to summarize these data is to construct a(n)
contingency table.
A(n) _______ variable is characterized by infinitely uncountable values and can take any value within interval.
continuous
A random variable X with an equally likely chance of assuming any value within a specified range is said to have which distribution?
continuous uniform distribution
When a researcher examines quantitative data and wants to know the number of observations that fall below the upper limit of a particular class, the researcher is BEST served by creating a ______.
cumulative frequency distribution
Generally, a person who is risk averse
demands a reward for taking risk.
Your business statistics class had a test last week. The average score for the class is an example of
descriptive statistics.
Let X = the side showing when a die is rolled. X is assumed to follow a uniform distribution because
each value of X has the same probability.
Due to symmetry, the probability that the standard normal random variable Z is greater than 0 is
equal to 0.5
A subset of the sample space is called a/an ______.
event
Using the multiplication rule, the probability that event A and event B both occur is computed by multiplying the conditional probability of event A given event B by the probability of
event B.
The Poisson random variable counts the number of occurrences of an event over a given interval of time or space while the ______ distribution describes the time that elapses between such occurrences.
exponential
For a continuous random variable X it is only meaningful to calculate the probability that the value of the random variable
falls within some specified interval.
A professor's marital status (married, single), as well as his/her rank (assistant, associate, full), represents ordinal data.
false
In the broadest sense, we can define the study of statistics as the methodology of extracting non-useful information from a data set.
false
True or false: The term central location relates to the way qualitative data tend to cluster around a lower value.
false
In descriptive statistics, a polygon is best described as a
graph that connects the midpoints of each class and its associated frequency or relative frequency.
Chebyshev's theorem provides the proportion of observations that lie within k standard deviations of the mean. The value k must be ______.
greater than 1
A z-score measures
how many standard deviations a value is from the mean.
If two events do not influence each other, then the events are ______ events.
independent
A continuous random variable has the uniform distribution on the interval [a,b] if its probability density function f(x)
is constant for all x between a and b, and 0 otherwise.
A random variable X follows the continuous uniform distribution if
it has an equally likely chance of assuming any value within a specified range.
The total probability rule is used to compute the probability of an event by using
joint probabilities. conditional probabilities.
A stem-and-leaf diagram has two parts: The stem and the leaf. The stem consists of the ______ and the leaf consists of the ______.
leftmost digits; digit to the right of the stem
The interval scale of data measurement is
less sophisticated than the ratio scale.
For a z-value less than 0, the P(Z<z) will be
less than 0.5.
The P(z1<Z<z2), where z1 and z2 are both positive and z1<z2, must be
less than 0.5.
The variance for probability distribution measures spread around the
mean
What is the most widely-used measure of central location?
mean
The average of the absolute differences between the values of the data set and the mean is the
mean absolute deviation.
The normal distribution is completely described by these two parameters:
mean and variance
A noted feature of the exponential distribution is that it is ___________ thus implying a constant failure rate.
memoryless
The ______ is a measure of central location that is the most frequently occurring value in the data set.
mode
The ordinal scale of data measurement is
more sophisticated than the nominal scale.
The variance for any discrete random variable is found by weighting the squared deviations about the mean by the respective probabilities. This can be simplified for the binomial random variable by
multiplying the number of trials by the probability of a success and the probability of a failure.
The expected value for any discrete random variable is found by summing up the product of the values of the random variables and their respective probabilities. This can be simplified for the binomial random variable by
multiplying the probability of a success by the number of trials.
For a binomial random variable X, the probability of x successes in n Bernoulli trials is calculated as
n!x!(n−x!)n!x!(n-x!)px(1-p)n-x
Classes are mutually exclusive if
no data value can fit into more than one class.
A recent survey of 200 small firms (with 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." This data is best classified as
nominal scale.
The exponential distribution is based entirely on
one parameter.
Differences between categories are meaningless with _____ data.
ordinal
A respondent of a survey is asked whether the Philadelphia Flyers' performance in the last game was excellent, good, fair, or poor. The person indicates that the performance was "good." This is an example of
ordinal data.
At the end of a semester, college students evaluate their instructors by assigning them to one of the following categories: Excellent, Good, Average, Below Average, and Poor. The measurement scale in this situation is a(n)
ordinal scale.
A Poisson random variable describes the number of successes of a certain event
over a given interval of time or in space.
The expected value of a distribution is also referred to as the
population mean.
If the covariance between two random variables x and y is positive, then x and y have a(n) _____.
positive linear relationship
A scatterplot is a type of graph that allows researchers to examine the relationship between two variables. It helps to identify
positive relationships. linear relationships. negative relationships. nonlinear relationships.
The probability distribution that describes a discrete random variable is called a
probability mass function.
A cumulative relative frequency distribution for quantitative data identifies the
proportion of observations that fall below the upper limit of each class.
A function that assigns numerical values to the outcomes of a random experiment is called a ______.
random variable
An analyst collects data on the weekly closing price of gold throughout a year. The scale of this data is
ratio
What is the scale of measurement of the distance between Houston and Dallas?
ratio
When calculating the probability of x successes in n trials of a binomial experiment, the probability of success and the probability of failure
remain the same, even when a probability is calculated for a different value of x.
Mean-variance analysis is used to measure the performance of an asset based on its rate of return. Specifically, this means evaluating the rate of return on the basis of
risk and reward.
The third quartile is the
same as the 75th percentile.
A softball coach believes that Laurie has a 0.25 probability of getting a hit against a particular pitcher that Laurie has never batted against before. What method was used to assign this probability?
subjective probability.
A normal random variable X is transformed into Z by ______.
subtracting the mean, and then dividing by the standard deviation.
For a continuous random variable, P(a≤X≤b) equals
the area under f(x) from a to b.