Sampling basics
What is the name for a number that describes a population?
PARAMETER
what symbol represents a sample proportion?
P-HAT
what symbol represents sample mean?
x-bar
What does CLT say about the sample means?
The sampling distribution of x-bar becomes approx normal as n increases.
what does 10% condition check?
The sample is small relative to the population (n < or equal to 10% of N)
What do we call the distribution of a statistic over all possible samples of the same size from a population?
Sampling distribution.
what is the mean of the sampling distribution of p-hat?
The population proportion, P
what is the mean of the sampling distribution of x-bar?
The population mean
what is the min sample size for CLT to apply in most cases?
30
why is randomness important in sampling distributions?
To ensure unbiased and valid results.
What is the difference between a statistic and a parameter?
A statistic describes a sample; a parameter describes a population.
what condition must be met for the std. dev formula for p-hat to be valid?
the 10% condition (sample size must be less then the 10% condition.
A population has a mean of 70 and a std dev of 12. what is the std dev of the sampling distribution of a sample mean for a sample size of 36?
12/square root 36= 12/6= 2!!
Can CLT be applied if the pop distribution is strongly skewed?
YES, if the sample size is large enough. ( greater then 30)
A sample size of 40 has p=0.6. Do the large counts condition apply?
np=40(0.6)=24, n(1-p)= 40(0.4)=16 YES.
what type of bias occurs when a sample does not represent the population?
Sampling bias.
what are the large counts condition?
n greater then or equal to to 10. and n(1-p)greater then or equal to to 10.
When can we say the sampling distribution of x-bar is approx normal?
If the population is normal or if n is greater then 30.
What happens to the std dev of x-bar as sample size increases?
It decreases in size.
You are sampling 50 students from a school of 600, does the 10% condition uphold in this situation?
Yes, 50<10% of 600.
True or false: the shape of the population affects the shape of the sampling distribution for the sample mean.
True(unless the sample size is large enough for the CLT to be applied.)
A population proportion is 0.4 and the sample size is 50. Find the std. Deviation of the sampling distribution of p-hat.
= 0.0693
A population has mean of 100 and a std dev of 20 find the std dev of the sampling distribution of x bar for n=25
20/5= 4
explain how the CLT justifies the use of normal probability calculations for non-normal populations.
As N increases, the sampling distributions of x-bar becomes more normal regardless of population shape, allowing us to use normal models.
A pop is right skewed. You take a normal sample of size 20. Can you use the normal model for x bar?
No, Because the sample is not large enough and the population is NOT normal.