Chapter 6 and Chapter 7 Flashcards
A continuous probability distribution for which the probability that the random variable will assume a value in any interval is the same for each interval of equal length.
Uniform Probability Distribution
A continuous probability distribution that has a probability density function that is bell-shaped and determine by its mean μ and standard deviation σ.
Normal Probability Distribution
A normal distribution what a mean of zero and a standard deviation of one.
Standard Normal Probability Distribution
A continuous probability distribution that is useful in computing probabilities for the time it takes to complete a task.
Exponential Probability Distribution
A function used to compute probabilities for a continuous random variable. The area under the graph of this function over an interval represents probability.
Probability Density Function
A numerical characteristic of a population, such as a population mean μ, a population standard deviation σ, a population proportion p, etc.
Parameter
A sample characteristic, such as a sample mean x bar, a sample standard deviation s, a sample proportion p bar, etc.
Sample Statistic
The value of a sample statistic used in a particular instance as an estimate of a population parameter.
Point Estimate
A property of a point estimator that is present when the expected value of the point estimator is equal to the population parameter it estimates.
Unbiased
The population for which the statistical inferences such as point estimates are made.
Target Population
The population from which the sample is taken.
Sampled Population
A property of a point estimator that is present whenever larger sample sizes tend to provide point estimates closer to the population parameter.
Consistency
Given two unbiased point estimators of the same population parameter, the point estimator with the smaller standard error is more efficient.
Relative Efficiency
The population from which the sample is taken.
Sampled Population
Once an element has been included in the sample, it is returned to the population. A previously selected element can be selected again and therefore may appear in the sample more than once.
Sampling with Replacement
Once an element has been included in the sample, it is removed from the population and cannot be selected a second time.
Sampling without Replacement
A sample of size n from a finite population of size N is selected such that each possible sample of size n has the same probability of being selected.
Simple Random Sample
A probability sampling method in which the population is first divided into strata and a simple random sample is then taken from each stratum.
Stratified Random Sampling
A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter.
Systematic Sampling
A probability sampling method in which the population is first divided into clusters and then a simple random sample of the clusters is taken.
Cluster Sampling
A nonprobability method of sampling whereby elements are selected for the sample on the basis of ease of collection.
Convenience Sampling
A nonprobability method of sampling whereby elements are selected for the sample based on the expertise of the person doing the study.
Judgment Sampling
A probability distribution consisting of all possible values of a sample statistic.
Sampling Distribution
The standard deviation of a point estimator.
Standard Error
The term that is used in the formulas whenever a finite population, rather than an infinite population, is being sampled.
Finite Population Correction Factor
A theorem that enables one to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large.
Central Limit Theorem
The Excel function that returns the standard normal distribution.
NORM.S.DIST
The Excel function that returns the inverse of the standard normal cumulative distribution.
NORM.S.INV
The Excel function that returns the normal distribution for the specified mean and standard deviation.
NORM.DIST
The Excel function that returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
NORM.INV
The Excel function that returns the exponential distribution.
EXPON.DIST
The Excel function that rounds a number down.
ROUNDDOWN
The Excel function that rounds a number up.
ROUNDUP
The Excel function that returns a random number greater than or equal to 0 and less than 1, evenly distributed.
RAND()
Name 3 continuous probability distributions.
Uniform Probability Distribution
Normal Probability Distribution
Exponential Probability Distribution
f(x) = 1/(b-a) for a <= x <=b f(x) = 0 elsewhere
Uniform Probability Density Function
E(x) = (a+b)/2
Expected Value of a Uniform Probability Distribution
Var(x) = (b-a)^2 / 12
Variance of a Uniform Probability Distribution
The most important distribution for describing a continuous random variable. It is widely use in statistical inference for applications such as heights of people, tests scores, rainfall amounts, scientific measurements, etc.
Normal Probability Distribution
Which probability distribution has a skewness measure of zero (i.e. it is symmetric).
Normal Probability Distribution
Normal probability distributions are defined by its _________ and ___________ .
Mean
Standard Deviation
The highest point on the normal curve is at the _______ / _______ / _______ .
Mean
Median
Mode
The _________ determines the width of the normal curve.
Standard Deviation
The empirical rule states that _____ % of values of a normal random variable are within +/- 1 standard deviation of its mean.
68%
The empirical rule states that _____ % of values of a normal random variable are within +/- 2 standard deviation of its mean.
95%
The empirical rule states that _____ % of values of a normal random variable are within +/- 3 standard deviation of its mean.
99.7%
The letter ___ is used to designate the standard normal random variable.
z
z = (x-μ)/σ
The formula for z-scores. Used to convert a normal probability distribution to a standard normal probability distribution.
The probability distribution used to describe time between vehicle arrivals at a toll booth, time required to complete a questionnaire, distance between major defects in a highway, etc.
Exponential Probability Distribution
For an exponential distribution, the ________ and ________ are equal.
Mean
Standard Deviation
The probability distribution that is skewed to the right.
Exponential Probability Distribution
An entity on which data are collected.
Element
A collection of all the elements of interest.
Population
A subset of the population.
Sample
The population from which the sample is drawn.
Sampled Population
A list of the elements from which the sample will be selected.
Frame
Some examples of ________ populations are: organization membership rosters, credit card account numbers, inventory product numbers, etc.
Finite
Some examples of _______ populations are: parts being manufactured on a production line, transactions occurring at a bank, telephone calls arriving at a technical help desk, etc.
Infinite
A form of statistical inference in which data from the sample are used to compute a value of a sample statistic that serves as an estimate of a population parameter.
Point Estimation
_____ is the point estimator of the population mean μ.
X Bar
_____ is the point estimator of the population standard deviation σ.
S
_____ is the point estimator of the population proportion p.
P Bar
The population about which we want to make inferences.
Target Population
The population from which the sample is actually taken.
Sampled Population
The probability distribution of all possible values of the sample mean x bar.
Sampling Distribution of X Bar
E(x bar) = ?
Population Mean μ
When the sample size is increased, the standard error of the sample mean is increased / decreased.
Decrease
The probability distribution of all possible values of the sample proportion p bar.
Sampling Distribution of P Bar
E(p bar) = ?
Population Proportion p
In stratified random sampling, the best results are obtained when the elements in one stratum form a heterogeneous / homogeneous group.
Homogeneous
In cluster sampling, ideally, the elements in each cluster form a heterogeneous / homogeneous group.
Heterogeneous
Name 4 probability sampling methods.
Simple Random
Stratified
Cluster
Systemic
Name 2 nonprobability sampling method.
Convenience
Judgment
