Flashcards in Exam 2 - Probabilities and sampling distribution Deck (53):

0

## Random phenomenon

### A phenomenon where the outcome of one play is unpredictable, but the outcomes from many plays form a distribution

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## Probability of an outcome is the

### Proportion of times that an outcome occurs in many, many repetitions(plays) of the random phenomenon.

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## In single random phenomenon the outcome is

###
Uncertain

Will the next flight to NY leave on time?

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## In many, many repetitions the proportion of specific outcomes is

###
Predictable

What proportion of flights to NY leave on time?

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## Randomness does NOT mean

###
Haphazard (disorganization)

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## SRS imposes .... chance of selection for each individual in the population

### Equal

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## Sample space in probability is

### The list of all possible outcomes of a random phenomen

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## Event in probability is a

### Single outcome or a subset of outcomes from the sample space

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## Probability model is a

### Mathematical description of a random phenomenon consisting of a sample space and a way of assigning probabilities to events.

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## Probability explains only what happens in the .... run

### Long

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##
If all probabilities are EQUALLY LIKELY, we need to count:

1.

2.

And that would be our probability

###
Count of outcomes in event of interest /

Over

Count of outcomes in sample space

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##
Probability rule 1

Probability must be a number

### Between 0 and 1

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##
Probability rule 2:

The sum of probabilities from all

### Possible outcomes must equal 1

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##
Probability rule 3

If two events cannot occur simultaneously, ...

### The probability either one or the other occurs equals the sum of their probabilities

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##
Probability rule 4:

The probability that an event does not occur equals

### 1 minus the probability that the event does occur

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## Disjoint Events

### Two events that have no outcomes in common and, thus cannot both occur simultaneously.

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## "Playing the game" or simulation means

### Looking at the phenomena many many times

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## Census

### An examination of entire population

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## Census is time consuming, very expensive and often impractical. What is the alternative?

###
1. Select SRS from population and compute x-bar(mean)

2. Make inference -

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## Parameter

###
Values that represent whole population. In statistical practice, the value is not known because we cannot examine the entire population.

Mean (mu), sigma and Proportion P

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## Parameter - mean

### Mu - mean number of cigarets smoked per day by ALL teenagers

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## Parameter of population P

### Proportion of ALL teenagers who used tobacco in the last 30 days

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## Statistic (think real world)

###
Values that come from a SAMPLE, statistics estimate parameters.

X-bar -sample mean

P-hat - sample proportion

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## Sample mean

###
X-bar

Mean number of cigarettes smoked per day in a SAMPLE of teenagers

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## Sample proportion

### P- hat proportion of a SAMPLE of teenagers who used tobacco in the last 30 days

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## In inference we use .... to estimate ..,

### Statistics to estimate parameter

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##
Statistics

Mean -

Proportion -

Standard deviation -

###
X- bar

P- hat

S

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##
Parameter

Mean

Proportion

Standard deviation

###
Mu

P

Sigma

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## What is statistical estimation?

### Using sample statistics to estimate population parameter value

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## Parameter is the result summarized from the

### Entire population

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## Statistic is any number result summarized from the

### Sample

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## If the response variable is quantitative we analyze ...

### Mean x-bar

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## If the response variable is categorical we analyze ...

### Proportion p

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##
Law of Large Numbers

IF .....

Then ...

### Draw observations at random from any population with finite mean mu. As the number of observations drawn increases, the mean x- bar of the observed values gets closer and closer to the mean mu of the population

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## The larger the sample size, the .... the sample mean is to the population mean

### Closer

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##
Sample statistic facts:

1. Value of statistic...

2. Value of statistic almost...

3. Statistic approaches...

###
1. Varies from sample to sample

2. Always differs from parameter values

3. Parameter value as sample size increases (the law of large numbers)

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## How do we investigate the behavior of statistic?

### By examining the sampling distribution of statistic

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## Theoretical sampling distribution of x- bar is

### The distribution of ALL x- bar values from ALL POSSIBLE SAMPLES of the same size from the same population

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##
Theoretical sampling distribution of x- bar

1. Take

2. Compute

3. Approximate

###
1. Take many, many SRSs

2. Compute x- bar for each

3. Approximate the theoretical sampling distribution of x- bar

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## Approximate sampling distribution of x- bar is

###
The distribution of x- bar values obtained from repeatedly taking SRSs. Of the same size from the same population.

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## Approximate sampling distribution of x-bar can be modeled with .... curve

### Normal

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##
How to determine how accurate is the sample mean as an estimator of mu?

1. Take...

2. Construct...

3. Note ...

###
1. Take many,many SRSs, compute x- bar for each sample

2. Construct histogram of x-bars to display the approximate sampling distribution of x- bar

3. Note center, spread and shape

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## Mean of all sampling distributions of x- bar =

### Mean of population

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## As n increases, spread of sampling distribution of x- bar

### decreases

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## As n increases, shape of sampling distribution of x- bar becomes

### More normal

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##
In sampling distributions

Center ... to population center regardless of sample size

### Equal or X- bar=mu

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## In sampling distributions as spread decreases n ...

### Increases

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## In sampling distributions the shape becomes ..... ....... as n increases

### More normal

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## How well does x-bar estimate mu?

### Quite well for large SRSs

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## Does x- bar vary about mu?

### Yes

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## Probability is measured on 0 to 1 scale , where 0 is .... And 1 is....

###
0 impossible , never occur

0.01 unlikely but occur once in a while in a long run

0.45 slightly less often than not

0.50 half of the time

0.55 slightly greater than one- half

0.99 greater than one half but less 1

1 - certain, will occurs every time

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## Population distribution

### The distribution of values of a variable among all individuals in the population

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