AP STATS 7.2 AND 7.3 - SAMPLE
PROPORTIONS // SAMPLE MEANS
Exam prep
Sampling Distribution of the Sample Mean - correct answersa probability distribution of all possible
sample means of a given sample size
sample mean symbol - correct answersx̅ (x-bar)
What happens when several samples are drawn from a population? - correct answersThey are likely to
have different values for x̅.
Why is x̅ considered a random variable? - correct answersBecause its value varies each time a sample is
drawn.
What can be computed for each value of the random variable x̅? - correct answersA probability.
What is the probability distribution of x̅ called? - correct answersThe sampling distribution of x̅.
population mean symbol - correct answersμ
population standard deviation symbol - correct answersσ
population mean formula - correct answersμ = ∑X / N
population standard deviation formula - correct answerssum of [ (value minus population average)
squared] divided by population number
What is the mean of the sampling distribution denoted by? - correct answersμx̅
What does the mean of the sampling distribution equal? - correct answersThe mean of the population
(μ)
What is the standard deviation of the sampling distribution sometimes called? - correct
answersStandard error
What is the formula for the standard deviation of the sampling distribution? - correct answersσx̅ = σ/√n
σx̅ = - correct answersσ/√n
μx̅ = - correct answersμ (sample mean)
What is the Central Limit Theorem? - correct answersIt is a fundamental theorem in Statistics that
describes the behavior of the sampling distribution of the sample mean.
, What does the Central Limit Theorem state about the sampling distribution of x̅? - correct answersThe
sampling distribution of x̅ is approximately normal for a large sample from any distribution.
What does the Central Limit Theorem state about the mean of a large simple random sample? - correct
answersThe sample mean x̅ has an approximately normal distribution with mean μx̅ = μ and standard
deviation σx̅ = σ/√n.
What is the sample size requirement for the Central Limit Theorem to apply? - correct answersThe
sample size should be large (n > 30).
When can a smaller sample size suffice for the Central Limit Theorem? - correct answersA smaller
sample size may suffice for symmetric populations.
What is the distribution of the sample mean x̅ if the population is normal? - correct answersThe sample
mean x̅ will be normal for any sample size.
You Should Know . . . - correct answersHow to construct the sampling distribution of a sample mean
How to find the mean and standard deviation of a sampling distribution of x̅
The Central Limit Theorem
How to use the Central Limit Theorem to compute probabilities involving sample means
The probability distribution of begin bar x end bar is called a ____ distribution - correct answerssampling
_______ states that the sampling distribution of begin bar x end bar is approximately normal when the
sample is large. - correct answersCentral Limit Theorem
The standard deviation of the sampling distribution is also called the - correct answersstandard error of
the mean
If we are finding a probability about xˉ (sample mean), so we use the - correct answerssampling
distribution of the mean
n = - correct answerssample size
A sample of size 126
will be drawn from a population with mean 26 and standard deviation 3
(a) Find the probability that begin bar x will be greater than 25 . Round the answer to at least four
decimal places. - correct answersσ = σ/√n
σ = 3/√126
μ = 26
use the normalcdf
- lower: 25
- upper: 9999 (because we want > 25)
PROPORTIONS // SAMPLE MEANS
Exam prep
Sampling Distribution of the Sample Mean - correct answersa probability distribution of all possible
sample means of a given sample size
sample mean symbol - correct answersx̅ (x-bar)
What happens when several samples are drawn from a population? - correct answersThey are likely to
have different values for x̅.
Why is x̅ considered a random variable? - correct answersBecause its value varies each time a sample is
drawn.
What can be computed for each value of the random variable x̅? - correct answersA probability.
What is the probability distribution of x̅ called? - correct answersThe sampling distribution of x̅.
population mean symbol - correct answersμ
population standard deviation symbol - correct answersσ
population mean formula - correct answersμ = ∑X / N
population standard deviation formula - correct answerssum of [ (value minus population average)
squared] divided by population number
What is the mean of the sampling distribution denoted by? - correct answersμx̅
What does the mean of the sampling distribution equal? - correct answersThe mean of the population
(μ)
What is the standard deviation of the sampling distribution sometimes called? - correct
answersStandard error
What is the formula for the standard deviation of the sampling distribution? - correct answersσx̅ = σ/√n
σx̅ = - correct answersσ/√n
μx̅ = - correct answersμ (sample mean)
What is the Central Limit Theorem? - correct answersIt is a fundamental theorem in Statistics that
describes the behavior of the sampling distribution of the sample mean.
, What does the Central Limit Theorem state about the sampling distribution of x̅? - correct answersThe
sampling distribution of x̅ is approximately normal for a large sample from any distribution.
What does the Central Limit Theorem state about the mean of a large simple random sample? - correct
answersThe sample mean x̅ has an approximately normal distribution with mean μx̅ = μ and standard
deviation σx̅ = σ/√n.
What is the sample size requirement for the Central Limit Theorem to apply? - correct answersThe
sample size should be large (n > 30).
When can a smaller sample size suffice for the Central Limit Theorem? - correct answersA smaller
sample size may suffice for symmetric populations.
What is the distribution of the sample mean x̅ if the population is normal? - correct answersThe sample
mean x̅ will be normal for any sample size.
You Should Know . . . - correct answersHow to construct the sampling distribution of a sample mean
How to find the mean and standard deviation of a sampling distribution of x̅
The Central Limit Theorem
How to use the Central Limit Theorem to compute probabilities involving sample means
The probability distribution of begin bar x end bar is called a ____ distribution - correct answerssampling
_______ states that the sampling distribution of begin bar x end bar is approximately normal when the
sample is large. - correct answersCentral Limit Theorem
The standard deviation of the sampling distribution is also called the - correct answersstandard error of
the mean
If we are finding a probability about xˉ (sample mean), so we use the - correct answerssampling
distribution of the mean
n = - correct answerssample size
A sample of size 126
will be drawn from a population with mean 26 and standard deviation 3
(a) Find the probability that begin bar x will be greater than 25 . Round the answer to at least four
decimal places. - correct answersσ = σ/√n
σ = 3/√126
μ = 26
use the normalcdf
- lower: 25
- upper: 9999 (because we want > 25)
