[L3] Samples, Populations, and the Normal Distribution

Question 1

In ___, we need to make sure, as far as
we can, that our sample is an unbiased and representative
sample of our population.

Answer 1

Inferential Statistics

Question 2

we also need to make sure that our sample is ___
enough.

Answer 2

large

Question 3

___– the “gold standard” to which other
sampling techniques aspire.

Answer 3

Random Sampling

Question 4

Two Conditions for Random Sampling to be satisfied:

Answer 4

equi-probability and independence

Question 5

every member of the population
must have an equal chance of being selected.

Answer 5

Equi-probability –

Question 6

– the selection of any one member of the
population should not affect the chances of any other
being selected.

Answer 6

Independence

Question 7

In practice it is very
___ to carry out RS!

Answer 7

difficult

Question 8

Random Sampling is

Answer 8

virtually impossible

Question 9

sampling methods

Answer 9

Volunteer sample
Snowball sampling
Purposive sampling
Convenience sampling

Question 10

The Importance of the Normal Distribution

Answer 10

Many variables that can be measured on a continuous
scale are (approximately) normally distributed.
* Many statistical tests make the assumption that our data
are normally distributed.

Question 11

Many ___ that can be measured on a continuous
scale are (approximately) normally distributed.

Answer 11

variables

Question 12

The area under the curve is equal to the ___

Answer 12

number of people
in that area.

Question 12

Where we have a histogram represented as a line chart,
with continuous variable on the x-axis (and where the yaxis
represents the frequency density), we can calculate
the number of people who have any score, or range of
scores, by calculating the ____

Answer 12

area of the chart.

Question 13

Many ____ make the assumption that our data
are normally distributed.

Answer 13

statistical tests

Question 14

The Normal Distribution goes on to
___ in each
direction.

Answer 14

infinity

Question 15

There is no _
_
_
__ to the x-axis, on a normal
distribution plot, at least in theory.

Answer 15

beginning and end

Question 16

The great advantage of a normal distribution is that if you
know (or can estimate) two values
__
_ you know everything there is to know about
it.

Answer 16

(Mean and Standard
Deviation),

Question 17

A score that is presented in terms of the number of
standard deviations above the mean is called a
__

Answer 17

z-score.

Question 18

A score that is presented in terms of the number of
___ above the mean is called a z-score.

Answer 18

standard deviations

Question 19

To calculate a z-score, we use the formula:
__

Answer 19

z = score – mean / σ (standard deviation)

Question 20

A z score is a transformed score that designates how many
___ the corresponding raw score is
above or below the Mean.

Answer 20

Standard Deviation units

Question 21

– process by which the raw score is
altered

Answer 21

Score transformation

Question 22

The z transformation results in a distribution having a
____

Answer 22

Mean of 0 and an SD of 1.

Question 23

Z scores allow us to determine the ____ any score in the
distribution.

Answer 23

number or percentages
of scores that fall above or below

Question 24

Z scores allow ____ between scores in different distributions, even when the units of distributions are different.

Answer 24

comparison,

Question 25

Important use –

Answer 25

comparing scores that are not otherwise directly comparable.

Question 26

the ability to compare scores that are measured on ___is of fundamental importance to the topic of ___.

Answer 26

different scales ; correlation

Question 27

Z scores have the ___ as the set of raw scores. Transforming the raw scores into their corresponding z scores does not change the shape of the distribution.

Answer 27

same shape

Question 28

The scores do not change their __. All that changes are the ___

Answer 28

relative positions; score values.

Question 29

The mean of the z scores always equals ___. The scores located at the mean of the raw scores will also be at the mean of the z scores.

Answer 29

zero

Question 30

The SD of z scores always equals to __

Answer 30

1

Question 31

_distribution of means from a set of samples. It is a listing of all the values the mean can take, along with the probability of getting each value if sampling is random from the null hypothesis population.

Answer 31

Sampling distribution of the mean –

Question 32

* Tells us that, given some assumptions, the sampling distribution of the mean will form a ____with a large sample

Answer 32

Central Limit Theorem; normal distribution,

Question 33

With a smaller sample, the distribution will be_

Answer 33

t-shaped.

Question 34

Statistical tests do not assume that the distribution of the data in the sample is ___.

Answer 34

normal

Question 35

Instead, it assumes that the ___ in the population is normal

Answer 35

sampling distribution of the sample means

Question 36

The CLT tells us that if the distribution in the sample is ___, then the sampling distribution will be the ___

Answer 36

approximately normal; correct shape.

Question 37

If the sample distribution is not normal, but the sample is large enough, then the sampling distribution will still be normal __

Answer 37

(or t-shaped)

Question 38

The ___ the sample, the __ we need to worry about whether our sample data are normally distributed or not.

Answer 38

larger; less

Question 39

___ _ – standard deviation of the sampling distribution of the mean.

Answer 39

Standard Error ( se )

Question 40

The Standard Error should be affected by the ___

Answer 40

Sample Size.

Question 41

The bigger the sample, the closer our sample mean is likely to be to the ____

Answer 41

population mean.

Question 42

– to make the point that the normal curve is a theoretical curve that is mathematically generated.

Answer 42

Formula

Question 43

We calculate the area under the curve, which will give the number of people, which will give the ___

Answer 43

probability of the range of responses.

Question 44

Formula for Area of Triangle

Answer 44

* W x H x 0.5

Question 45

Probability of scores =

Answer 45

area of the small triangle divided by the area of the large triangle

Question 46

There is a ___ that we use to calculate the area under the normal curve, for any value taken from the normal distribution, and we can use this to calculate the probability of any range of responses.

Answer 46

formula

Question 47

This means we can use the area under the curve to find the ___

Answer 47

probability of any value or range of values.

Question 48

In a normal distribution ___ of the scores will lie above the mean and ___ below the mean.

Answer 48

half, half

Question 49

If we take a sample from a population and calculate the mean for that sample, we are likely to find a value close to the mean for the ___.

Answer 49

population

Question 50

* It is very ____ that we will hit the true (population) mean and we might, if we are very unlucky, find a value far from the true (population) mean.

Answer 50

unlikely

Question 51

We are just as likely to ___ the population mean as we are to overestimate the population mean.

Answer 51

underestimate

Question 52

This indicates that the mean is ___.

Answer 52

unbiased

Question 53

The _____states that the sampling distribution of any statistic will be normal or nearly normal, if the sample size is large enough

Answer 53

central limit theorem

Question 54

How large is "large enough"? The answer depends on two factors.

Answer 54

1. Requirements for accuracy. 2. The shape of the underlying population.

Question 55

The more closely the sampling distribution needs to resemble a normal distribution, the more sample points will be required.

Answer 55

Requirements for accuracy.

Question 56

The more closely the original population resembles a normal distribution, the fewer sample points will be required.

Answer 56

The shape of the underlying population.

Question 57

if there is a lot of variation in the sample, there will be more uncertainty in the sample, so there will be more uncertainty about the population mean.

Answer 57

Amount of Variation in Sample –

Question 58

: contains the z score.

Answer 58

Column A

Question 59

lists the proportion of the total area between a given z score and the mean.

Answer 59

Column B:

Question 60

: lists the proportion of the total area that exists beyond the z score.

Answer 60

Column C