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23 Cards in this Set
 Front
 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 1020 is large enough 

How large does N need to be for a skewed distribution? 
2540 

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 1020. If the sample size is less than 1020, 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 2540. Ifthe sample size is less than 2540, 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 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 pvalue is < alpha, reject the null: there is evidence that the population mean is ________ is less than/ greater than/ or different than the null. If pvalue 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. 