5-Distributions of Statistics

Question 1

What is the (sampling) distribution of means ?

Answer 1

A probability distribution of all possible sample means computed from samples of the same size.

Question 2

What is sampling with or without replacement ?

Answer 2

With, each time a score is drawn from a population it is returned to population before the score is drawn. Without, the score is not returned before the drawn of the next score

Question 3

What does N^n means ?

Answer 3

N, the number of scores in a population and n , the number of score in the sample

Question 4

True or false: the mean of the distribution of means (µm) will always equal the mean of the population of scores

Answer 4

True

Question 5

What does E stands for ? What does E(m) stands for ?

Answer 5

The expected value : The mean of a statistical distribution

Question 6

True or false. E(m) = µ.

Answer 6

True. It is an unbiased estimator of its parameter

Question 7

We call a statistic unbiased, when … ?

Answer 7

its expected value equals the parameter it estimates.

Question 8

What is the formula for the variance of the distribution of means ?

Answer 8

om^2/n

Question 9

What is the standard error of the means (SEM) ? What is the formula ?

Answer 9

the squared root of the variance of the distribution of means

om= squ.rt. of om^2/n OR om= o/squ.rt. n

it is the equivalent of the standard deviation

Question 10

How do you calculate SEM in an interval ?

Answer 10

mew+-σ/squ.rt of n

Question 11

True or false. The larger the sample, the better it estimates

Answer 11

True

Question 12

Why does σm is called the standard error of the mean instead of the standard deviation of the mean ?

Answer 12

Because σm is rougly the average sampling error (the difference between sample’s statistic and the parameters it estimates)

Question 13

What is the formula for the average sampling error and standard error of the mean ?

Answer 13

average sampling error: S[mi-mew]/Nm

σm= squ.rt. of S(m-mew)^2/Nm

Question 14

What is the formula for the average sampling error and standard error of the mean ? Whats the difference between the two ?

Answer 14

average sampling error: S[mi-mew]/Nm

σm= squ.rt. of S(m-mew)^2/Nm

The standard error of the mean is ROUGHLY the average sampling error. So we consider more the average samplir error as a formula

Question 15

Whats the difference between standard deviation and standard error ?

Answer 15

Standard deviations : average distance between scores and the mean

Standard error : Average distance between the statistics and the parameters they estimate

Question 16

What is the central limit theorem ?

Answer 16

It states (roughly) that the distribution of means will be a normal distribution if the population being sampled is normal. It also states that the distribution of sample means will converge on a normal distribution as sample size increases,

Question 17

What is the rule of thumb for a normal sample size

Answer 17

Have 30+ for a normal distribution of means