Flashcards in Exam 2-3 Deck (12):

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## Central Limit Theorem

### When sampling from a non-Normal population, the sampling distribution of x bar is approximately Normal whenever the sample is large and random

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## Sample

### A subset of individuals in the population; the group about which we actually collect information.

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## Theoretical sampling distribution of x bar

### The distribution of all possible samples of the same size from the same population

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## Approximate sampling distribution of x bar

### The distribution of x bar values obtained from repeatedly taking SRS's of the same size from the same population

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##
Sampling distribution of x bar

1. Center

2. Spread

3. Shape

###
1.mean of x bar = population mean valid for all sample sizes and populations of all shapes

2. Stand.deviation of x bar= stand dev of population decided by the square root of n

3. Normal -shape of x bar distribution is exactly normal for any n; Non-Normal - shape of sampling distribution of x bar is approximately normal when n (sample size) is large

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## Facts about Sampling Distribution of x bar

###
-Mean= mu regardless of population shape or sample size

- standard dev of x bar is always less than the standard deviation of the population for samples of any size where n>1

-standard dev of x bar gets smaller as n increases at rate square root of n. To cut stand dev in half, quadruple sample size

- Shape is normal if population is normal for any sample size

- shape is approximately Normal if we take a large random sample from a non-normal population

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## Standard deviation if x bar ( standard deviation of the sampling distribution of x bar)

### A measure of variability of the values of the statistic x bar about mu ; a measure of the variability of the sampling distribution of x bar; in other words the average amount that statistic (x bar) deviates from it's mean. Computed as sigma over square root of n

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## Predicting sampling distribution of x bar

###
Take only one sample of size n

Use results to make inference about the population

Because mean =mu and standard deviation of x bar= sigma over square root of n; and the shape is approx Normal if sample is random and large according to CLT

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## R-sq is a fraction of

### Variation in the values of y that is explained by the least squares regression of y on x

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## Outlier in y direction of a Scatterplot have ...... Residuals but other outliers need not to have large residuals

### Large

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## Influential observations in x direction of Scatterplot are often ..... For the least-squares regression line

### Influential

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