6: Sampling Distributions I

Question 1

Law of Large Numbers

Answer 1

If we draw independent observations at random from any population with finite mean (u) as the number of observations drawn increases, the mean of the observed values (x-bar) eventually approaches u.

OR, as the number of randomly drawn observations n in a sample increases, the mean of the sample gets closer and closer to the TRUE popln mean u

Question 2

parameter

Answer 2

true value of a population quantity which we don’t know in practice

Question 3

sampling distribution

Answer 3

distribution of values taken by the statistic in all possible samples of the same size from the same population

Question 4

sampling variability

Answer 4

the value of a sample statistic will vary in a repeated random sampling

Question 5

population distribution

Answer 5

the popln distribution of a variable is the distribution of its values for all members of the population

also, the probability distribution of the variable when we choose one individual from the population at random

Question 6

sampling distribution of the mean - mean and std. dev

Answer 6

for a sampling distribution, the standard deviation is called the standard error

= std dev / sqr rt n

Question 7

Central Limit Theorem

Answer 7

Draw a SRS of size n from any population with mean μ and finite standard deviation σ.

When n is large, the sampling distribution of the sample mean is approximately normal: N(μ, σ/√n).

Question 8

binomial distribution for sample counts

Answer 8

probability of distribution of a random variable that can take on one of two possible variables

Question 9

binomial setting (4 rules)

Answer 9

1. fixed number of trials
2. in each trial, a certain outcome can occur - success or failure
3. probability of success remains constant from trial to trial (p of failure also constant)
4. n trials are all independent