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Flashcards in Exam 2-3 Deck (12):
0

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

1

Sample

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

2

Theoretical sampling distribution of x bar

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

3

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

4

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

6

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

7

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

8

R-sq is a fraction of

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

9

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

Large

10

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

Influential

11

To add categorical variable to Scatterplot

Add different color or symbol for each category