Exam 2- sampling distributions Flashcards
Approximate sampling distribution of x- bar is
The distribution of x- bar values obtained from repeatedly taking SRSs of the same size from the same population
Theoretical sampling distribution of x- bar is
The distribution of all x- bar values from all possible samples of the same size from the same population
Center
The mean of the sampling distribution of x- bar …. the mu….
Equals ….. Population mean
Mean =mu is valid for
All sample sizes and populations of all shapes
Spread
The standard deviation of the sampling distribution of x- bar …..
Equals the standard deviation of the population divided by the square root of n
Valid for all sample sizes and population of all shapes
Shape
For non-normal population
Shape of sampling distribution of x-bar is approximately normal when n is large
Shape
For normal population
Shape of the sampling distribution if x- bar is exactly normal for any n
Mean …… equals mu regardless of population shape or sample size
Exactly
Standard deviation of x- bar is always ….. Than the standard deviation of the population for samples of any size where ….
Less. n>1
Standard deviation of c- bar gets ….as n increases at rate ….
Smaller…. Square root of n
To cut standard deviation in half
Quadruple sample size
Shape is normal if population is …..for any sample size
Normal
Shape is approximately normal if we take a …… ……. ……. from a non- normal population
Large random sample
The population distribution of a variable is
The distribution of values of the variable among all the individuals in the population
The sampling distribution of a statistic is
The distribution of values taken by the statistic in all possible samples of the same size from the same population
The population distribution describes the ….. that make up the population
Individuals
A sampling distribution describes how …. Varies in many samples from the population
Statistic
What is distribution of random variable?
A list of all possible values of a variable together with how often each value occurs
The probability of an event can be defined as
The fraction of time the event will occur if random phenomenon is related many time
Central Limit Tgeorem
If you take a large SRS of size n from any population then the sampling distribution of x- bar is approximately not mail
The central limit theorem on x- bar requires
A large random sample
A correlation of r=0 indicates
That x and y are not linearly related
T/F probabilities on individuals can only be computed using the standard Normal table if the population is Normally distributed
True
What does the probability distribution of a random variable gives us?
All possible values if the random variable together with their probabilities
T/F because there is a probability assigned to each event, the probability model is correct
T
T/f because all probabilities are between zero and one, and because the sum of all probabilities is 1, the probability model is correct
True
The law of the large numbers refers to the …. Of a ….. Not to the sampling distribution of x- bar
Mean of a sample
What does the Law of Large numbers tell us?
As sample size increases, the variable x-bar from a random sample gets closer and closer to mu
The mean x-bar of all possible samples will exactly equal to the population mean or would that a mean of a sampling distribution x-bar that would be equal mu?
The mean of the sampling distribution will equal mu
