Midterm (also look at 1 and 2)

Question 1

z-scores

Answer 1

Tell us how many SDs a score is above or below the mean

z = deviation/ standard deviation

Question 2

Standard normal distribution

Answer 2

• Perfectly symmetrical
• Bell-shaped: high probability in the center and lower probability in tails
• Area under it is = to 1; collectively all scores have a proportion = to 1 (percent = 100)
• Mean, median, mode are at center of distribution
• The tails (away from center) are asymptotic
• Defined by mathematical formula- a model for data of -
  many variables
• Areas under it are known

Question 3

Probability

Answer 3

For a random event, a ratio- a number of ways the event can occur divided by the total number of possible events (sample space)
p (x) = f (x) / sample space

Question 4

Properties of sample probabilities

Answer 4

Total range from 0 to 1
- 0 means event is impossible
- 1 means the event is certain
Can never be negative
- Either possible or impossible

Question 5

What is the difference between relative frequency and probability?

Answer 5

probability helps us PREDICT what could happen (whereas rf tells us what has already happened)

Question 6

Probability Distributions

Answer 6

Goal: interest in knowing the probability of each possible outcome of a random variable
Sum of probabilities is 1

Also interested in:
Expected values- mean or avg. expected outcome of a random variable
The variance and standard deviation of a probability distribution- avg (typical) distance of outcomes from the expected value

Question 7

2 goals of inferential statistics

Answer 7

Make unbiased estimates
Assess error made when making estimates
— Sampling Dist. does this

Question 8

Sampling goal

Answer 8

obtain a subset of population that represents population

use random sampling

• Each element in pop. has = chance of being chosen
• Each selection is independent of other selections

Question 9

sampling error

Answer 9

estimation of parameters involves this

Question 10

Sampling Distribution

Answer 10

Distribution of a STATISTIC derived from all possible samples of a given size

Can imagine it but can never see it (because we don’t have all of the data)
But it is useful for:
- Establishing the rationale for estimation of population parameters from statistics
- Assessing the amount of error we are likely to make when using a statistic to estimate a parameter

Question 11

Unbiased estimator

Answer 11

A statistic, over all possible samples of a given size, has a mean value = to the pop. parameter
Proven that:
M is an unbiased estimator of μ
- in the long run overestimates are offset by underestimates

Question 12

Standard error

Answer 12

We could determine the typical amount of error we could expect to make by calculating SD of relevant sampling distribution

the SD of the sampling distribution

Question 13

standard error of the mean

Answer 13

standard error for an estimate of the mean

Sm is an unbiased estimator of the typical amount of error made when using M to estimate μ

Question 14

how do we get an unbiased estimator of pop. variance and SD?

Answer 14

By dividing degrees of freedom (n - 1) instead of sample size (n)

Question 15

Degrees of freedom

Answer 15

the # of ways something is free to vary (the # of independent pieces of info needed to determine a statistic

For measures of variability (s2 and s), df = n –1, because once all but one deviation from the mean is known, the last one is set (is no longer free to vary)