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.