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23 Cards in this Set

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  • Back

Population Mean and Standard Deviation

ū= mean; Ō= standard deviation

Sample Mean and Standard Deviation

ȳ= mean; s= standard deviation

Sampling Distribution

ō÷√n

Required Assumptions

-Randomization


-10% condition


-Nearly Normal

How large does N need to be for a symmetric distribution?

Usually 10-20 is large enough

How large does N need to be for a skewed distribution?

25-40

As the sample size gets larger, what characteristics change to the distribution model?

-Shape gets closer to a normal model


-The mean stays approximately equal to the population mean


-The standard deviation decreased based on the sampling distribution formula

If the population distribution is normal, then the sample distribution and sampling distribution will be?

Normal

Ifyou know the population distribution is not normal butsymmetric,the sample distribution will have a...?

Similar shape as the population, and the sampling distribution will likely be normal if the sample size is at least 10-20. If the sample size is less than 10-20, it is possible that the sampling distribution will be symmetric but not quite normal.

Ifyou know the population distribution is skewed, thesample distribution will be..?

Skewed, and the sampling distribution will likely be normal if the sample size is at least 25-40. Ifthe sample size is less than 25-40, it is likely that thesampling distribution will be skewed but not as skewed as the population.

Sampling Distributions: Statistics- Proportions vs. Means

Proportions: use p hat; Assumptions: randomization, success/failure, and 10%




Means: use y bar; Assumptions: randomization, 10%, and nearly normal condition.

Sampling Distributions: Standard Deviation- Proportions vs. Means

Proportions: √p(1- p)/n




Means: ō/√n

How to standardize a sampling distribution

Y bar- mean/ standard deviation/√n

DF

(n- 1)

Confidence Interval for Mean

Y bar ± t∗ (s/√n)

As the CI increases does the t∗ increase or decrease?

Increases

In order to increase the width and the margin of error, what happens to t∗?

It also increases

As the sample size increases, t∗ decreases

True

Example

1) Random sample


2) 10%: A sample of _____ is less than 10% of the population size.


3) Nearly Normal Confidence: Sample size is sufficiently large or not sufficiently large enough for the sampling distribution to be approximately normal


4) df
5) t∗


6) Y bar ± t∗ (s/√n)


7) We are __% confident that the population mean number of ________ is between ______ and ______

Hypothesis Tests

H₀: µ= µ₀

HA: µ< µ₀


HA: µ > µ₀


HA: µ ≠ µ₀

Hypothesis Tests for µ

Assumptions are the same for CI:


Assumptions: Randomization Condition, 10%, and Nearly Normal Condition

If the null hypothesis is true...

t= Y bar - µ₀/(s/√n)

Rejecting and Failing to Reject the Null

If p-value is < alpha, reject the null: there is evidence that the population mean is ________ is less than/ greater than/ or different than the null.


If p-value is > alpha, fail to reject the null: there is not evidence that the population mean is _______ is less than/ greater than/ or not equal to the null.