BNAD 276
normally distributed. in order to transform a standard normal value z into its unstandardized values x, we use the following formula:
x=mean +z standard deviation
average growth rate (calculating)
1. use the geometric mean which analyzing a multi-year investment
if p平均 is the value that a normal random assumes, then we can transform it into its standard normal values as
Z=(p平均－p)/ root p(1-p)/n
classical probability
a probability based on logical analysis
experiment
a trial, or process, that produces several possible outcomes
quantitative variables
a variable that assumes meaningful numerical values
one of the primary goals when constructing a frequency distribution for quantitative data is summarize the data in a manner that
accurately depicts the data as a whole
a significant weakness of the ordinal scale is
an inability to measure differences between the ranked value because the actual numbers used are arbitrary
generally, a person who is risk neutral
bases decision solely on the basis of expected values
suppose you were told the delivery time of your new washing machine is equally likely over the time period 9 am to noon. If we define the random variable X as delivery time, then X follow the
continous uniform distribution
the total area under the normal curve is__
equal to 1
b/(a=b)
given odds against event A occurring of "a to b", the probability of A
scatterplot
hep in determining whether or nor two quantitative variables are related in some systematic way
descriptive statistic
it refers to the summary of important aspects of a data set.
for a continuous random variable X, the cumulative distribution function F(x) provides the probability that X is
less than or equal to any value x
due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to___p9Z
p(Z﹤-1.5)
the expected value of P平均 is the
proportion of successes in the population
relative frequency distribution for quantitative data identifies the
proportion/fraction of observations that occur in each class
the probability distribution of the sample mean is commonly referred to as the___
sampling distribution of x average
Standard deviation
square root of the average of the sum of squared deviations from the mean is known as the
addition rule is used to calculate
the union of two events
a parameter is a numerical measure that describes a population
true
the probability that a continuos variable X assumes a particular values x is
zero
variable
a characteristic of interest that differs among various observation (when a characteristic of interest differs in kind or degree among various observations, then the characteristic can be termed a variable)
estimate
a particular value of the estimator
what is a primary requirement for a "good" sample?
it is representative of the population we are trying to describe
multiplication rule
it states that the probability that A and B both occur is equal to the probability that A occurs given that B has occurred times the probability that B occurs.
the measure of central location
median (best), mean, mode
for qualitative data set, the most meaningful measure of the central location is the___
mode
when summarizing a qualitative data set, the___is the best measure of central location
mode
nominal /ordinal
nominal:at least the sophisticated form of data ordinal: are stronger in the sense that we categorize and order the data
which of the following is an example of a continuous random variable?
normal random variable
sharpe ratio determines the additional ____ an investor will receive for each additional unit of risk taken
reward
mean-variance analysis is used to measure the performance of an asset based on its rate of return. Specifically, evaluating the rate of return on the basis of
risk and reward
when the finite population correction factor is applied to the sample proportion, the resulting standard error for the sample proportion is equal to
root(P(1-P)/n) * root (N-n)/(N-1)
a population consists of all items of interest in a statistical problem, whereas a___ is a subset of the population
sample
if we were to sample repeatedly from a given population, the average value of the sample means will equal______
the population mean
if two events are independent, then the probability that both events occur equals
the product of the individual probabilities
ratio scale
the strongest level of measurement. ti has all the characteristics of interval data as well as a true zero point, which allows us to interpret the ratios of values. a ratio is used to measure many types of data in the business analysis
in a give cumulative frequency distribution, the "cumulative frequency" column value for the third class represents
the sum of observation in the first, second, third classes
what does it mean when we say that the tails of the normal curve are asymptotic to the x axis?
the tails get closer and closer to the x axis but never touch it
Bias can occur in sampling, Bias refers to
the tendency of a sample statistic to systematically over/under-estimate a population parameter
variance
the variance measures the dispersion of the spread of the data, not the central location
statistic is used
to make informed decisions based on data
if you have data that describes the entire population, then there is no need to make inferences using sample data.
true
chebyshev's theorem is applicable
when the data are any shape
which of the following is considered an estimate?
x平均=20
capital z is used to denote the standard normal random variable
z
the complement rule with respect to event A is
P(Ac)=1-P(A)
the stander deviation of x average is =
SD/root random sample
coefficient of variation (sample CV/Population
Sample: s/v population: population std deviation/population mean
the expected values of the discrete random variable X is
a weighted average of all possible values of X
Stem-and leaf diagrams can be used to
analyze the shape the data determine how dis[ersed the data is observe individual data points
polygon histogram stem-and-leaf diagram
are useful to observe the shape(distribution) of a data set for a single variable
the probability that a discrete random variable X assumes a particular values x is
between zero and one
the numerical measure that reveals only the direction of the liner near relationship between two variables, but not the strength of the linear relationship, is referring to as the ____
covariance
correlation coefficient
describes both the direction and the strength of the linear relationship between two random variables
expected values of the sample proportion is
equal P
mutually exclusive events
events that cannot both occur on the same trial of an experiment
summarize qualitative data
frequency distribution
a/(a=B)
given odds for event A occurring of "a to b," the probability of A is
the sample size required to approximate the normal distribution depends on
how much the population varies from normality
simple random sampling
in the simple random sampling, the population is not divided into groups
for a continuous random variable X, how many distinct values can it assume over an interval?
infinite
cluster sampling
involves dividing a population into mutually exclusive and exhaustive groups
simple random sample
is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
continuous variable
is characterized by uncountable values within an interval, weight, height, time and investment return are all example.
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 o otherwise
discrete variable
it assumes a countable number of values
Chebyshev's Theorem should only be applied to data sets that are normally distributed
it can be used an approximation for many real-world applications
sample space
it denoted by S, of an experiment contains all possible outcomes pf the experiment
random variable
it is a function that assigns numerical values to the outcomes of an experiment
ogive
it is a graph that plots the cumulative frequency, or cumulative relative frequency, against the upper limit of the corresponding class
Coefficient variation
it is a relative measure of dispersion and adjusts for differences in the magnitudes of the means
histogram
it is best used to display the relative frequency of grouped, quantitative data
subjective probability
it is calculated by drawing on personal and subject judgment
weighted mean
it is relevant when some observations contribute more than others
variance
it is the average of the squared deviations from the mean.
median character
it is the best measure of central location when outlines are presents
conditional probability
it is the probability of an event given that another event has already occured
time series data
it refers to data collected by recording a characteristic of a subject over several time periods. it can include hourly, daily, weekly, monthly, quarterly or annual observation.
cross-sectional data
it refers to data collected by recording a characteristic of many subjects at the same point in time, or without regard to differences in time.
inferential statistics
it refers to drawing conclusions about a large set of data called a population-based on a smaller set of small data
nominal scale
it represents the least sophisticated level of measurement. if we are presented with nominal data, all we can do is categorize or group the data. the values in the data set differ merely by name or label.
samples are primarily used to
make inferences about population parameters
the probability distribution of a continuous random variable is called its
probability density function
how to decided the range
range=MAX-MIN
the central limit theorem states that the distribution of the sample mean will be approximately normal if
the sample size is sufficiently large; as a general guideline n 大于等于30
selection bia occurs when
there is a systematic exclusion of certain groups from consideration for the sample
empirical probability
this event is the observed relative frequency with which an event occurs (observed data)
stratified sampling is preferred to cluster sampling when the objective is
to increase precision
to calculate the union for two mutually exclusive events A and B
we add the probability of A to the probability of B
it is referred to as an estimator
when a statistic is used to estimate a parameter
calculate the mean absolute deviation?
1. calculate the arithmetic mean 2. find the absolute difference between each value and the mean 3. sum the absolute differences 4. divided by the sample or population
when a box post is constructed, an outlier is a data point that is farther than____
1.5*IQR form Q1 or Q3
probability
A numerical value that measure the likelihood of an uncertain event
population
A population includes all items of interest in a statistical problem.
event
A subset of the sample space
addition rule for mutually exclusive
if A and B are mutually exclusive events, the (P(A交B)=0, the addition rule simplifies to P(A并B)=P(A)+P(B)
what kind of sampling is more likely to be used by political pollsters who want to ensure that each religious group is represented in the sample?
stratified random sampling (because although a simple random sample can be representative of a population, have a stratified random samples is better because it ensures that each ethnic group, religious group, etc, it included in the sample
a softball coach believes that Laurie has a 0.5 probability of getting a hit against a particular pitcher that Laurie has never batted against before
subjective probability
the area under a normal curve below its expected value is_____
0.50
1. the standard deviation of the sample mean 2. the expected value of the sample mean 3. the variance of the sample mean
1. SD/root n 2. mean 3. SD^2/n
the intersection of events A and B, denoted A并B, contain
all outcomes that are in A and B
covariance
an objective numerical mesure that reveals the direction of the linear relationship between two variables
the shape of the grog depicting the normal probability density function is___
bell shaped
the central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes_____
closer to a normal distribution
ordinal scale
compare to the nominal scale, it reflects a stronger level of measurement. it can able to both categorize and rank the data with respect to some characteristic or trait. the weakness.
relative frequency distribution are generally more useful than frequency distribution when
comparing data sets of different sizes
Bernoulli process
consists of a series of n independment and identical trials of the experiment such that on each trial: only two possible outcomes, success and failure
example of the continuous uniform distribution
delivery time of an appliance, the scheduled flight time of two cities, and the waiting time for a campus bus
generally, a person who is risk averse
demands a reward for taking risk (needs a grater reward in order to engage in the risky transaction)
bar chart
depicts the frequency or relative frequency for each category of the qualitative variable as a series of horizontal or vertical bars, the length of which are proportional to the values that are to depicted
event are exhaustive
if all possible outcomes of an experiment belong to the events
mutually exclusive
if they do not share any common outcome of an experiment
the expected value of x平均 is equal to mean
important point need to know
we can use the finite population correction factor when
n大于等于0.05N
it is known that the length of a certain product X is normally distributed with std=20 inches. how is the probability P9x
p(X＞16) is greater than p(x﹤16)
it is known that the length of a certain product X is normally distributed with std=20 inches how is the P(X﹤20) related tot he P(X﹤16)
p(x﹤20( is greater than P(x﹤16)
if the covariance between two random variables x and y is positive, then X and Y have a ____
positive linear relationship
if X is a normally distributed random variable, then
the mean, the median, and the mode are all equal
all of the following are examples of random variables that likely follow a normal distribution EXCEPT:
the number of states of the USA (this is not a varibale)
Stratified random sampling
the population is divided up into mutually exclusive and collectively exhaustive groups called strata. the sample consists of elements from each stratum.
