Sampling Distribution Flashcards
A sample
Is a part of a population used to represent the population
The population
Is the complete set of items of interest
Population parameters
Population mean μ
Population standard deviation σ
Statistics
Sample mean x
Sample standard deviation s
Statistics are used to…
Make inferences about population parameters
Statistics vary depending on….
The particular sample chosen
The sampling distribution is unbiased if…
It’s mean (x) is equal to the associated population parameter (μ)
Means are ______ measurements
Proportion are essentially ________ measurements
Quantitative
Qualitative
How to find the standard deviation of a sample proportion
_________
s= ✔️(p(1-p))/n)
To use normal approximation for a binomial proportion, np and n(1-p) should be at least ___
10
To use normal approximation for a binomial proportion, it is important that samples are _________
Simple random samples
To use normal approximation for a binomial proportion, the sample size should be no larger than…
10% of the population
This actually show indep, but the simple random sample requirement allows us to assume independence
How to find the standard deviation of a sample mean (x)
s= _σ__
(✔️n)
While giving the mean (x) and standard deviation (s) of a set of sample means, we do not describe….
The shape of the distribution
Because we can only conclude that the sample is normal if the population is normal
No matter how the original population is distributed, if……. The set of sample means is approximately normally distributed
n is large enough (30)
Aka central limit theorem
Distribution of the original population
May be uniform, bell-shaped, strongly skewed, etc.
Standard deviation of two sample proportions
s= p1(1-p1) + p2(1-p2)
✔️ n1 n2
The mean of the set of difference of sample proportions equals….
p1-p2
The difference of the population proportions
The standard deviation of a set of differences of sample means is approximately…
σ1^2 + σ2^2
✔️ n1 n2
The more either population varies from normal, the greater should be the corresponding ______
Sample size
*but should still be less than 10% of the population
When to use t distributions
When the population standard deviation (σ) is unknown and the original pop is normally distributed
How to find t
t= __x-μ__
s/(✔️n)
t distributions are associated with…
Degrees of freedom (df)
df= n-1
He last row of Table B (for t distributions) is the ______
Normal distribution, which is the case of the t-distribution taken when n is infinite
Why are t distributions used so often?
The real world σ is almost always unknown
The issue of sample size refined by statisticians:
The t-distribution with an SRS with large n (>40)
Unnecessary to make any assumptions about parent population
The issue of sample size refined by statisticians:
The t-distribution with an SRS with medium n (15-40)
Sample should show no extreme values and little, if any, skewness; or assume parent population is normal
The issue of sample size refined by statisticians:
The t-distribution with an SRS with small n (<15)
Sample should show no outliers and no skewness; or assume parent population is normal
What are chi square models used for?
Tests (not confidence intervals)
Chi square parameter
Degrees of freedom
df= n-2
With chi square, if df is small the distribution is…
Skewed right
With chi square, if df is small the distribution….
Becomes more symmetric and bell-shaped. (Like a t distribution)
With chi square, for one or two df the peak occurs at ___
Zero
With chi square, for 3+ df! the peak is at…
df-2
Chi square distributions are _________ distributions
Continuous
Applying it to counting data is just an approximation
Standard error of a proportion
SE(p)= pq
✔️ n
Standard error for means
SE(x)= s
(✔️n)
If the population is not normally distribution, does the sampling distribution of x have a mean equal to the population mean?
Yes
The sampling distribution of p
The population proportion (p)
If data from a sample is skewed left, what happens when the sample size goes from n=50 to n=200?
The mean stays the same
The standard deviation becomes smaller
The shape becomes closer to normal
Why is the sample. Axiom not used as an estimator for the population maximum?
The sample maximum is biased
t distributions are always ______
Symmetric and mound shaped
Like normal distributions
