Lesson 11 - Sampling Distributions

DEGREES OF FREEDOM

NORMAL

For the student's t-distribution, as the __________ increases, the distribution approaches a standard _______ distribution.

FIVE

NORMAL

If X is a binomial random variable and both np and n(1−p) are both greater than _____ then we can approximate the distribution of X using a ______ distribution with a mean of np and a standard deviation of sqrt[np(1−p)].

standard deviation

sqrt[np(1-p)] is the _____ for a binomial random variable

mean

np is the _____ for a binomial random variable

standard deviation

sqrt(λ) is the _____ for a Poisson random variable

mean

λ is the _____ for a Poisson random variable

FIVE

NORMAL

If X is a Poisson random variable and λ is greater than _____ then we can approximate the distribution of X using a ______ distribution with a mean of λ and a standard deviation of sqrt(λ).

INDEPENDENT

RANDOM SAMPLE

A set of n _______ random variables X₁,X₂,...,X_n with the same distribution are called a _____________.

STATISTIC

The probability distribution of a ______ (calculated from a sample) is called its sampling distribution.

SAMPLE

The probability distribution of a statistic is calculated from a ________.

POPULATION

The mean or expected value of the sample mean, x̄, is equal to the ______ mean μ and the standard deviation of the sample mean, x̄, is equal to σ divided by THE SQUARE ROOT OF THE SAMPLE SIZE.

sample mean

EXACTLY

If the population is normal then the distribution of the sample mean will be _______ normal.

APPROXIMATELY

If the population is NOT normal but the sample size is large enough then the distribution of the sample mean will be __________ normal.

INFERENCE

Sampling distributions allow us to perform statistical _________.

PARAMETERS

HYPOTHESIS

Using the results of sampling distributions we can:

• Estimate unknown _______ with a specified confidence level

• Conduct _____ tests about parameters to compare them to target values

standard deviation of the sampling distribution of x̄

Normal Approximations to Binomial and Poisson