Flashcards in Stat - Exam #2 Deck (90)

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1

## What is the Sampling Distribution of the Statistics?

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-Stats calculated from a sample varies with each sample;

-Variation because each stat is a random variable that follows some probability density CURVE with a LOCATION and SPREAD;

2

## What is Sampling Distribution?

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A probability density curve of all possible values of a statistic computed for a sample size (n).;

-Focus on the Population Means

3

## What is the Law of Large Numbers?

### As the sample size gets LARGER, the difference between the sample average and the population mean gets SMALLER

4

## What is affected by SAMPLE SIZE with normally distributed data?

### -Normally distributed, the MEAN of sample average is NOT affected by sample size, but the standard deviation of the sample average IS affect by size

5

## What is Sampling Distribution of Sample Average?

### If data are distributed normally with mean (u) and standard deviation (sigma), then the average of a sample of size (n) with be distributed normally with mean (u) and standard deviation [sigma/(sq. rt of n)]

6

## IF/THEN of Sampling Distribution of Sample Average

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IF: x has shape NOR with location (u) and spread (sigma)

THEN: x-bar has shape NOR with location (u) and spread {sigma/(sq. rt of n)}

7

## What is the Standard Error of the Mean?

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The standard deviation of the same average;

— sigma_x-bar = sigma/(sq. rt of n)

8

## How do you find the shape of a sample for data NOT normally distributed?

### -The sample average and the sample standard deviation can be calculated, but the shape is determined from a z-curve and the z-table = Central Limit Theorem

9

## What is the Central Limit Theorem?

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- When there are at least 30 data points (any shape, mean u, and standard deviation) the SAMPLE AVERAGE will...

1. follow the NORMAL shape

2. have mean (u) — same as population;

3. and have standard deviation {sigma/(sq. rt. of n)}

10

## LESS than 30 data points

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-Unknown shape;

-Mean (u);

-Standard deviation {sigma/(sq. rt. of n)}

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## Greater than or Equal to 30 data points

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-NORMAL shape;

-Mean (u);

-Standard deviation {sigma/(sq. rt. of n)}

12

## Difference in the Sampling Distribution and Central Limit Theorem

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Sampling distribution of the mean deals with the location and spread of the sample average;

-The central limit theorem deals only with the SHAPE of the sample average

13

## What is the population standard deviation is UNKNOWN?

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-Use the sample standard deviation to calculate confidence interval estimates of a population parameter;

-The sample standard deviation can be calculated ANYTIME there is a sample

14

## What is used to get degrees of freedom and critical values of the sample test?

### The t-table

15

## What do you calculate when the population standard deviation is UNKNOWN?

### -Replace the populations standard deviation with with SAMPLE standard deviation = t-transforation that yields a t-statistic

16

## What is a t-transformation?

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Converts a sample average into a t-statistic

t = (x-bar - u) / [s/(sq. rt of n)]

17

## What is t-distribution?

### If a simple random sample of size (n) is taken from a population that follows the normal distribution, then the t-statistic follows the t-distribution with (n-1) degrees of freedom

18

## What is a t-statistic?

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t _ (sigma/2), (n-1) =

- sigma/2 = gives the area in one tail = Column of t-table;

- n-1 give the degrees of freedom = Row of t-table

19

## How do you use the t-table?

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-Need to know the area under the tail and the degrees of freedom;

-If the exact are not in the table, follow the practice of always going down to the next lower degrees of freedom in the table;

-NOTE: the LAST row of that -table is the same as the z-table

20

## What is a reasonable value for the population mean?

### A CONFIDENCE INTERVAL gives a set of values that are reasonable choices for the population mean based on the information in the SAMPLE data

21

## Where does the level of confidence come from?

### The NORMAL probability curve

22

## What is Inferential Stats?

### Use the information from a sample to make conclusions about the population

23

## What is an Interval Estimate?

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-Value of sample stat is very seldom the exact population parameter, but pretty close;

-Calculate a sample stat and an INTERVAL indicating how close the stat is to the population parameter;

**Central to Inferential Stats

24

## What are the major methods of Inferential Stats?

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1. Confidence Interval Estimation = give an estimate of the value of the UNKNOWN population parameter;

2. Hypothesis Testing = Claim about a population, then sample data are collected and use to test this claim

25

## Which standard deviation is ALWAYS known?

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-Sample!;

- Population is not usually known in everyday practice

26

## What is required when the population standard deviation is UNKNOWN?

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Requires the used of a t-value

(Z-scores are only applicable when pop. standard deviation is already known)

27

## What is the Point Estimate of a population parameter?

### The value of the sample statistic used to estimate the population parameter

28

## What is the Point Estimate of of the population MEAN?

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The value of the sample average;

-BEST estimator of the population mean

Sample Average = POINT ESTIMATOR

Actual value of Sample Average = POINT ESTIMATE

29

## What is the Point Estimate of the population STANDARD DEVIATION?

### The value of the sample standard deviation

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