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Statistics > Exam 2 - Probabilities and sampling distribution > Flashcards

Exam 2 - Probabilities and sampling distribution Flashcards

0
Q

Probability of an outcome is the

A

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

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1
Q

Random phenomenon

A

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

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2
Q

In single random phenomenon the outcome is

A

Uncertain

Will the next flight to NY leave on time?

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3
Q

In many, many repetitions the proportion of specific outcomes is

A

Predictable

What proportion of flights to NY leave on time?

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4
Q

Randomness does NOT mean

A

Haphazard (disorganization)

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5
Q

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

A

Equal

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6
Q

Sample space in probability is

A

The list of all possible outcomes of a random phenomen

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7
Q

Event in probability is a

A

Single outcome or a subset of outcomes from the sample space

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8
Q

Probability model is a

A

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

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9
Q

Probability explains only what happens in the …. run

A

Long

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10
Q

If all probabilities are EQUALLY LIKELY, we need to count:
1.
2.
And that would be our probability

A

Count of outcomes in event of interest /
Over
Count of outcomes in sample space

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11
Q

Probability rule 1

Probability must be a number

A

Between 0 and 1

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12
Q

Probability rule 2:

The sum of probabilities from all

A

Possible outcomes must equal 1

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13
Q

Probability rule 3

If two events cannot occur simultaneously, …

A

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

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14
Q

Probability rule 4:

The probability that an event does not occur equals

A

1 minus the probability that the event does occur

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15
Q

Disjoint Events

A

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

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16
Q

“Playing the game” or simulation means

A

Looking at the phenomena many many times

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17
Q

Census

A

An examination of entire population

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18
Q

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

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

2. Make inference -

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19
Q

Parameter

A

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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20
Q

Parameter - mean

A

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

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21
Q

Parameter of population P

A

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

22
Q

Statistic (think real world)

A

Values that come from a SAMPLE, statistics estimate parameters.

X-bar -sample mean
P-hat - sample proportion

23
Q

Sample mean

A

X-bar

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

24
Q

Sample proportion

A

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

25
Q

In inference we use …. to estimate ..,

A

Statistics to estimate parameter

26
Q

Statistics
Mean -
Proportion -
Standard deviation -

A

X- bar
P- hat
S

27
Q

Parameter
Mean
Proportion
Standard deviation

A

Mu
P
Sigma

28
Q

What is statistical estimation?

A

Using sample statistics to estimate population parameter value

29
Q

Parameter is the result summarized from the

A

Entire population

30
Q

Statistic is any number result summarized from the

A

Sample

31
Q

If the response variable is quantitative we analyze …

A

Mean x-bar

32
Q

If the response variable is categorical we analyze …

A

Proportion p

33
Q

Law of Large Numbers

IF …..
Then …

A

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

34
Q

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

A

Closer

35
Q

Sample statistic facts:

  1. Value of statistic…
  2. Value of statistic almost…
  3. Statistic approaches…
A
  1. Varies from sample to sample
  2. Always differs from parameter values
  3. Parameter value as sample size increases (the law of large numbers)
36
Q

How do we investigate the behavior of statistic?

A

By examining the sampling distribution of statistic

37
Q

Theoretical sampling distribution of x- bar is

A

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

38
Q

Theoretical sampling distribution of x- bar

  1. Take
  2. Compute
  3. Approximate
A
  1. Take many, many SRSs
  2. Compute x- bar for each
  3. Approximate the theoretical sampling distribution of x- bar
39
Q

Approximate sampling distribution of x- bar is

A

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

40
Q

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

A

Normal

41
Q

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

  1. Take…
  2. Construct…
  3. Note …
A
  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
42
Q

Mean of all sampling distributions of x- bar =

A

Mean of population

43
Q

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

A

decreases

44
Q

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

A

More normal

45
Q

In sampling distributions

Center … to population center regardless of sample size

A

Equal or X- bar=mu

46
Q

In sampling distributions as spread decreases n …

A

Increases

47
Q

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

A

More normal

48
Q

How well does x-bar estimate mu?

A

Quite well for large SRSs

49
Q

Does x- bar vary about mu?

A

Yes

50
Q

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

A 
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
51
Q

Population distribution

A

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

52
Q

Sampling distribution

A

The distribution of values taken by a statistic in all possible samples of the same size from the same population

Statistics (14 decks)

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