Chapter 7 Flashcards
Population parameter
Quantitative- M or Mx
Porportion/cat-P or π
Population Standard deviation
Quantitative- σ or σx
Porportion/cat-none
M
quant opulation parameter
Mx
Quant population parameter
P
Porportional/cat population parameter
π
Porportional/cat population parameter
Sample statisctic
Quantitative- x̅
Porportion- p̂
σ
Quant standard deviation of population
σx
Quant standard deviation of population
Sample standard deviation
Quantitative- Sx
Porportion/Categorical- None
x̅
Quantitative sample statistic
p̂
Porportion/cat sample statistic
Mean of the sampling distribution
Quantitative- Mx̅
Porportion/Categorical- Mp̂
Sx
Quant sample standard deviation
Standard deviation of the sampling distribution
Quantitative- σx̅
Porportion/Categorical- σp̂
Mx̅
Quant mean of the sampling distribution
Mp̂
Porportion/cat mean of the sampling distribution
σx̅
Quant standard deviation of the sampling distribution
σp̂
Porportion/cat of standard deviation of the sampling distribution
Sampling distribution for quantitative center
Mx̅= M if the sample was selected in a random unbiased manner
Sampling distribution for porportion center
Mp̂= P if the sample was selected in a random unbiased manner
Sampling distribution for quantitative shape
Shape of sampling distribution is appprox normal if the sample size is sufficently large enough to overcome skewness in the populaiton
n=30 is sufficently large
n=1 is sufficently large for nomral populations
More skew in population means you need an bigger sample size for it to be normal
Sampling distribution for porportional shape
The sample size is sufficently large if:
np> or = 10
and
nq> or = 10
Sampling distribution for quantitative shape
σx = σ / sqrt(n).
If the population is sufficently large and n < 1/10 population
Sampling distribution for porporional shape
σp̂= Squart root(pq/n)
if the population is sufficently large and n < 1/10pop
Sampling distribution
Distribution of all possible statistics (x bars and p hats) of a specific sample size taken from a specific popualtion
Population distribution
Distribution of a variable of all individuals
Central limit theorem
As the sample size of only a sampling distribution increases and sample size is sufficently large,
- The shape of the sampling distribution becomes more normal
- The mean of the sampling distribution stays exactly the same
- The standard deviation of the sampling distribution decreases
How is the mean of a sampling distribution related to the true population mean for the distribution
It is exactly the same
How is the standard deviation of the sampling distribution related to the standard deviation of the population
Sampling distribution standard deviation is less than the standard deviation of the population
Will we ever know the true population parameters (like mean and standard deviation)
no
Would it be necessary to collect a sample from the population if you already know the population parameters you were interested in
No
How is our degree of confidence change in relation to the sample size of our sampling distribtion
If the sample size of the sampling distribution is larger, we are more confident in our estimate of the parameters due to the smaller standard deviation
How will the center of a sampling distribution change as the sample size n increases
It doesnt
How will the standard deviation of the sampling distribution change as the sample size increases
It decrease
Why are bigger sample sizes better for sampling distributions
They provide less sampling distribution while remaining unbiased (mean of the sampling distribution is equal to the mean of the population)
