Exam 2 - Probabilities and sampling distribution

Question 0

Probability of an outcome is the

Answer 0

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

Question 1

Random phenomenon

Answer 1

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

Question 2

In single random phenomenon the outcome is

Answer 2

Uncertain

Will the next flight to NY leave on time?

Question 3

In many, many repetitions the proportion of specific outcomes is

Answer 3

Predictable

What proportion of flights to NY leave on time?

Question 4

Randomness does NOT mean

Answer 4

Haphazard (disorganization)

Question 5

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

Answer 5

Equal

Question 6

Sample space in probability is

Answer 6

The list of all possible outcomes of a random phenomen

Question 7

Event in probability is a

Answer 7

Single outcome or a subset of outcomes from the sample space

Question 8

Probability model is a

Answer 8

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

Question 9

Probability explains only what happens in the …. run

Answer 9

Long

Question 10

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

Answer 10

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

Question 11

Probability rule 1

Probability must be a number

Answer 11

Between 0 and 1

Question 12

Probability rule 2:

The sum of probabilities from all

Answer 12

Possible outcomes must equal 1

Question 13

Probability rule 3

If two events cannot occur simultaneously, …

Answer 13

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

Question 14

Probability rule 4:

The probability that an event does not occur equals

Answer 14

1 minus the probability that the event does occur

Question 15

Disjoint Events

Answer 15

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

Question 16

“Playing the game” or simulation means

Answer 16

Looking at the phenomena many many times

Question 17

Census

Answer 17

An examination of entire population

Question 18

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

Answer 18

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

2. Make inference -

Question 19

Parameter

Answer 19

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

Question 20

Parameter - mean

Answer 20

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

Question 21

Parameter of population P

Answer 21

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

Question 22

Statistic (think real world)

Answer 22

Values that come from a SAMPLE, statistics estimate parameters.

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

Question 23

Sample mean

Answer 23

X-bar

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

Question 24

Sample proportion

Answer 24

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

Question 25

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

Answer 25

Statistics to estimate parameter

Question 26

Statistics Mean - Proportion - Standard deviation -

Answer 26

X- bar P- hat S

Question 27

Parameter Mean Proportion Standard deviation

Answer 27

Mu P Sigma

Question 28

What is statistical estimation?

Answer 28

Using sample statistics to estimate population parameter value

Question 29

Parameter is the result summarized from the

Answer 29

Entire population

Question 30

Statistic is any number result summarized from the

Answer 30

Sample

Question 31

If the response variable is quantitative we analyze ...

Answer 31

Mean x-bar

Question 32

If the response variable is categorical we analyze ...

Answer 32

Proportion p

Question 33

Law of Large Numbers IF ..... Then ...

Answer 33

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

Question 34

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

Answer 34

Closer

Question 35

Sample statistic facts: 1. Value of statistic... 2. Value of statistic almost... 3. Statistic approaches...

Answer 35

1. Varies from sample to sample 2. Always differs from parameter values 3. Parameter value as sample size increases (the law of large numbers)

Question 36

How do we investigate the behavior of statistic?

Answer 36

By examining the sampling distribution of statistic

Question 37

Theoretical sampling distribution of x- bar is

Answer 37

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

Question 38

Theoretical sampling distribution of x- bar 1. Take 2. Compute 3. Approximate

Answer 38

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

Question 39

Approximate sampling distribution of x- bar is

Answer 39

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

Question 40

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

Answer 40

Normal

Question 41

How to determine how accurate is the sample mean as an estimator of mu? 1. Take... 2. Construct... 3. Note ...

Answer 41

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

Question 42

Mean of all sampling distributions of x- bar =

Answer 42

Mean of population

Question 43

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

Answer 43

decreases

Question 44

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

Answer 44

More normal

Question 45

In sampling distributions | Center ... to population center regardless of sample size

Answer 45

Equal or X- bar=mu

Question 46

In sampling distributions as spread decreases n ...

Answer 46

Increases

Question 47

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

Answer 47

More normal

Question 48

How well does x-bar estimate mu?

Answer 48

Quite well for large SRSs

Question 49

Does x- bar vary about mu?

Answer 49

Yes

Question 50

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

Answer 50

``` 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 ```

Question 51

Population distribution

Answer 51

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

Question 52

Sampling distribution

Answer 52

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