Stats For Healthcare Exam 2

Front 1

What is a probability distribution for a discrete random variable?

Back 1

A mutually exclusive listing of all possible numerical outcomes for that variable such that a particular probability of occurrence is associated with each outcome.

Front 2

What is the mean of a probability distribution?

Back 2

the expected value of its random variable

Front 3

What is the covariance?

Back 3

Measure of the strength of the relationship between two discrete random variables, X and Y.

Front 4

What is the expected sum of two random variables?

Back 4

it is equal to the sum of the expected values

Front 5

What is the variance of the sum of two random variables?

Back 5

equal to the sum of the variances plus twice the covariance

Front 6

What is the standard devisation of the sum of two random variables?

Back 6

the square root of the variance of the sum of two random variables

Front 7

What is the rule of combinations?

Back 7

the number of ways of selecting X objects from n objects, irrespective of sequence

Front 8

What is the mean of the binomial distribution?

Back 8

equal to the sample size, n, multiplied by the probability of success

Front 9

What is the area of opportunity?

Back 9

a continuous unit or interval of time, volume, or such area in which more than one occurrence of an event can occur

Front 10

What is the Poisson distribution?

Back 10

a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event.

Front 11

When can you uses the Poisson distribution?

Back 11

1)when counting the # of times a part. event occurs in a given area of opportunity;(2)prob. that event occurs in a given area of opp. is the same for all the areas of opp.; (3) # of events in one area of opp. is indep. of the # of events that occur in any other area of opp.; (4) prob. that 2 or more events will occur in an area of opp. approaches 0 as the area of opp. becomes smaller

Front 12

What is the hypergeometric distribution?

Back 12

discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement

Front 13

What is the difference btwn a binomial and hypergeometric distribution?

Back 13

binomial dist. sample data selected with replacement from a finite pop. or without replacement from an infinite pop. Hyper dist. data selected without replacement from a finite pop.

Front 14

What is a continuous probability density function?

Back 14

mathematical expression that defines the distribution of the values for a continuous random variable

Front 15

What is a normal distrubtion?

Back 15

(Gaussian distribution) most common continuous distribution used in stats

Front 16

3 reasons normal distribution is important?

Back 16

(1)numerous cont. variables common in business have dist. that closely resemble the normal distribution; (2) normal dist. can be used to approximate various discrete prob. dist.; (3) normal dist. provides the basis for classical statistical inference b/c of it's relationship to the central limit theorem

Front 17

What is the normal probability density function?

Back 17

mathematical expression representing a continuous probability density function - denoted (f)X

Front 18

What is the transformation formula?

Back 18

when the Z value is equl to the difference between X and the mean divided by the standard deviation

Front 19

What is the cumulative standardized normal distribution?

Back 19

f

Front 20

What is an X value?

Back 20

equal to the mean plus the product of the Z falue and the standard deviation.

Front 21

What is a normal probability plot?

Back 21

graphical approach for evaluating whether data are normally distributed

Front 22

What is quantile-quantile plot?

Back 22

transforming each ordered value to a Z value and then plot the data values versus the Z values

Front 23

What is a uniform distribution?

Back 23

when a value has the same probability of occurrence anywhere inthe range between the smallest value, a, and the largest value, b. Sometimes called the rectangular distrubtion.

Front 24

What is the exponential distribution?

Back 24

continuous distrubution that is right skewed and ranges from zero to positive infinity

Front 25

What is a frame?

Back 25

a listing of items that make up the population; they are data sources such as population lists, directories, or maps (samples are drawn from frames)

Front 26

What is a nonprobability sample?

Back 26

when you select the items or individuals without k nowing their probabilities of selection

Front 27

What is convenience sampling?

Back 27

Type of nonprobability sampling - items are sleected based only on the fact that they are easy, inexpensive, or convenient to sample

Front 28

What is a judgment and sample?

Back 28

you get the opinions of preselected experts in the subject matter

Front 29

What is the probability sample?

Back 29

you select the items based on known probabilities

Front 30

What is a simple random sample?

Back 30

every item from the frame has the same chance of selection as every other item

Front 31

What is sampling with replacement?

Back 31

After you select an item, you return it to the frame where it has the same probability of being selected again

Front 32

What is sampling without replacement?

Back 32

Once you select an item, you cannot select it again

Front 33

What is a table of random numbers?

Back 33

consists of a series of digits listed in a randomly generated sequence

Front 34

What does a table of random numbers do?

Back 34

Because the numeric system uses 10 digits, the chance that you will randomly generate any particular digit is equal to the probability of generating any other digit.

Front 35

Systematic sample

Back 35

partition the N items in the fram into n groups of k items where... k=N/n

Front 36

Least efficient sampling methods

Back 36

simple random sampling and systematic sampling

Front 37

Stratified sample

Back 37

subdivide the N items in the frame into separate subpopulations, or strata

Front 38

What is a strata?

Back 38

some common characteristic, such as gender or year in school

Front 39

What is a cluster sample?

Back 39

divide N items in the frame into several clusters so that each cluster is representative of the entire population - more cost effective but requires larger sample size

Front 40

What is a cluster?

Back 40

naturally occurring designations, such as counties, election districts, city blocks, households, or sales territories

Front 41

4 types of survey errors

Back 41

coverage; nonresponsive; sampling; measurement

Front 42

What is a coverage error?

Back 42

occurs if certain groups of items are excluded drom this frame so that they have no chance of being selected in the sample

Front 43

What is a selection bias

Back 43

if the frame is inadequate because certain groups of items in the population were not properly included

Front 44

What does a table of random numbers do?

Back 44

Because the numeric system uses 10 digits, the chance that you will randomly generate any particular digit is equal to the probability of generating any other digit.

Front 45

Systematic sample

Back 45

partition the N items in the fram into n groups of k items where... k=N/n

Front 46

Least efficient sampling methods

Back 46

simple random sampling and systematic sampling

Front 47

Stratified sample

Back 47

subdivide the N items in the frame into separate subpopulations, or strata

Front 48

What is a strata?

Back 48

some common characteristic, such as gender or year in school

Front 49

What is a cluster sample?

Back 49

divide N items in the frame into several clusters so each cluster is representative of the entire population

Front 50

What is a cluster?

Back 50

naturally occurring designations, such as countries, election districts, city blocks, households, etc.

Front 51

Pros/cons with cluster samples?

Back 51

more cost effective but require larger sample size

Front 52

4 types of survey errors

Back 52

coverage; nonresponse; sampling; measurement

Front 53

What is a coverage error?

Back 53

certain grps of items excluded from this frame so no chance of being selected in sample

Front 54

What is a selection bias?

Back 54

frame is inadequate because certain groups of items in the population were not properly included.

Front 55

What is a nonresponse error?

Back 55

failure to collect data on all items in the sample

Front 56

What is a nonresponse bias

Back 56

certain groups left out of population

Front 57

How to avoid nonresponse error

Back 57

follow up with people who did not respond; use best mode for response (ie telephone, not mail)

Front 58

What is a sampling error?

Back 58

reflects the variation from sample to sample

Front 59

3 sources of measurement error

Back 59

ambiguous wording of questions
the halo effect
respondent error (can recall the the individuals with unusual responses and establish program of random callbacks)

Front 60

Ethical issues

Back 60

coverage: purposeful exclusion of particular individuals
nonresponse: sponsor knowingly designs survey so particular groups are less likely to respond
sampling error: findings are purposely presented without reference to sample size and margin of error
measurement: leading questions, creates halo effect or provides false info.

Front 61

Ethical issues in nonprobability sampling methods

Back 61

used to form conclusions about an entire population - must state the results cannot be generalized beyond the sample

Front 62

What is a sampling distribution?

Back 62

distribution of the results if you actually selected all possible samples

Front 63

What is the sampling distribution of the mean

Back 63

distribution of all possible sample means if you select all possible samples of a certain size

Front 64

What is the population mean?

Back 64

sum of the values in teh population divided by the population size, N.

Front 65

What is the standard error of the mean?

Back 65

how the means vary from sample to sample

Front 66

What is the Central Limit Theorem?

Back 66

states that as the sample size (# of values in each sample) gets large enough, the sampling distribution of the mean is approximately normally distributed. True regardless of the shape of the distribution of the individual values in the population

Front 67

What is a point estimate?

Back 67

value of a single sample statistic

Front 68

What is a confidence interval estimate?

Back 68

range of numbers, called an interval, constructed around the point estimate

Front 69

What reasoning is used in confidence interval estimation for the mean (known)

Back 69

inductive reasoning - use resulsts of a single sample to draw conclusions about a population

Front 70

What is the critical value?

Back 70

value of Z needed for constructing a confidence interval.

Front 71

Student's t distribution

Back 71

used when standard deviation is not known

Front 72

What is a null hypothesis?

Back 72

one of status quo and is identified by the symbol Ho

Front 73

What is the alternative hypothesis H1

Back 73

opposite of the null hypothesis

Front 74

If you reject the null hypothesis.....

Back 74

you have statistical proof that the alternative hypothesis is correct

Front 75

If you do not reject the null hypothesis.....

Back 75

you have failed to prove the alternative hypothesis. Failure to prove the alternative hypothesis, however, does not mean that you have proven the null hypothesis.

Front 76

The null hypothesis always....

Back 76

refers to a specified value of the population parameter such as the mean of the population, not a sample statistic sch as the mean of the sample

Front 77

The statement of the null hypothesis always.....

Back 77

continas an = regarding the specified value of the population parameter (Ho: pop. mean = 368 grams)

Front 78

The statement of the alternative hypothesis never....

Back 78

contains an equal sign regarding the specified value of the population parameter

Front 79

What is a test statistic?

Back 79

estimate of the corresponding parameter

Front 80

What is a region of rejection (critical region)?

Back 80

consists of values of test statistic that are unlikely to occur if the Ho is true.

Front 81

What are the two regions of the sampling distribution of the test statistic?

Back 81

region of rejection and region of nonrejection

Front 82

What is the critical value?

Back 82

divides the nonrejection region from the rejection region.

Front 83

How to determine critical value

Back 83

depends on size of the rejection region

Front 84

What is a Type I error?

Back 84

if you rejct the Ho when it is true and should not be rejected. P(Type I error is alpha)

Front 85

What is a Type II error?

Back 85

if you do not reject the Ho when it is false and should be rejected. P(Type II error is beta)

Front 86

What is the level of significance?

Back 86

Probability of committing a Type I error

Front 87

What is the confidence coefficient?

Back 87

1-alpha: probability that you will not rejct the Ho when it is true and should not be rejected.

Front 88

What is the confidence level?

Back 88

(1-alpha) x100%

Front 89

Dependent variable

Back 89

the variable you wish to predict

Front 90

Independent variable

Back 90

variables used to make the predictions

Front 91

Simple linear regression

Back 91

single numerical independent variable, X, is used to predict the numerical dependent variable, Y

Front 92

Scatter plot (scatter diagram)

Back 92

examines relationship between X on horizontal axis and Y on vertical axis - nature of relationship btwn these two can range from simple to extremely complicated

Front 93

Simple linear regression model

Back 93

consists of a straight-line

Front 94

Dependent variable

Back 94

the variable you wish to predict

Front 95

Independent variable

Back 95

variables used to make the predictions

Front 96

Simple linear regression

Back 96

single numerical independent variable, X, is used to predict the numerical dependent variable, Y

Front 97

Scatter plot (scatter diagram)

Back 97

examines relationship between X on horizontal axis and Y on vertical axis - nature of relationship btwn these two can range from simple to extremely complicated

Front 98

Simple linear regression model

Back 98

consists of a straight-line

Front 99

What is a slope?

Back 99

the expected change in Y per unit change in X

Front 100

What is the Y intercept?

Back 100

the mean value of Y when X equals 0

Front 101

What is a positive linear relationship?

Back 101

Y increases as X increases

Front 102

What is a negative linear relationship?

Back 102

Value of Y decreases as X increases

Front 103

What is a positive curvilinear relationship?

Back 103

Value of Y increases as X increases, but this increase tapers off beyond certain values of X

Front 104

What is a U-shaped curvilinear relationship?

Back 104

As X increases, at first Y generally decreases; but as X continues to increase, Y not only stops decreasing but actually increases above it's minimum value

Front 105

What is a negative curvilinear relationship?

Back 105

exponential relationship between X and Y - Y decreases rapidly as X first increases, but then it decreases much less rapidly as X increases further

Front 106

What is no relationship?

Back 106

High and low values of Y appear at each value of X

Front 107

What is the relevant range?

Back 107

includes all values from smallest to largest X used in developing the regression model

Front 108

What is a mathematical model?

Back 108

mathematical expression that represents a variable of interest

Front 109

What is the binomial distribution?

Back 109

When the discrete variable of interest is the number of successes in a sample of n observations.

Front 110

Essential properties of a binomial distribution

Back 110

1. fix # of observations in sample
2. is mutually exclusive and collectively exhaustive (success or faillure)
3. P(success) is constant from obser. to obser.
4. outcome is independent of the outcome of any other observation

Front 111

Name 3 discrete distributions

Back 111

binomial, poisson, hypogeometric

Front 112

Name 3 continuous distributions

Back 112

normal, uniform, and exponential

Front 113

What is the Poisson distrubtion?

Back 113

the probability of X events in an area of opportunity

Front 114

When to use Poisson distrubtion

Back 114

1) area of opportunity is defined by time, length, surface area (2) probability is the same for all areas of opportunity (3) independent of # of events that occur in any other area (4) prob of 2< events occurring approaches 0 as opportunity becomes smaller

Front 115

What is a discrete variable?

Back 115

produces outcomes that come from a counting process

Front 116

What is a continuous variable?

Back 116

produces outcomes that come from a measuring process

Front 117

Examples of discrete random variable

Back 117

number of mortgages approved each week; how many credit cards in wallet; number of interruptions per day

Front 118

What is a normal distribution?

Back 118

most common continuous distribution used in statistics (Gaussian distribution)

Front 119

What are characteristics of a normal distribution?

Back 119

1)continuous variables common in business have distributions closely resembling the normal distribution (2) used to approximate various discrete probability distributions (3) provides basis for classical statistical inference b/c of relationship to Central Limit Theorem

Front 120

What is the normal probability density function?

Back 120

f(X) - math. expression representng a continuous probability density fucntion

Front 121

What does the transformation formula do?

Back 121

converts any normal random variable, X, to a standardized normal random variable, Z.

Front 122

What is a uniform distribution?

Back 122

value that has the same probability of occurrence anywhere in the range between the smallest value, a, and the largest value, b. Because of its shape is sometimes called the rectangular distribution

Front 123

What is the exponential distribution?

Back 123

continuous distribution that is right-skewed and ranges from zero to positive infinity

Front 124

When is exponential distribution used?

Back 124

waiting line (or queuing) theory to model the length of time between arrivals in processes such as customers at a bank's ATM, patients entering ER, hits on web site.