Samples, Populations, and the Normal Distribution

Question 1

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

Answer 2

large enough

Question 3

Two Conditions for Random Sampling to be satisfied:

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

Answer 3

equi-probability

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:

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

Answer 4

independence

Question 4

Many variables that can be measured on a continuous
scale are (approximately)

Many statistical tests make the assumption that our data
are

Answer 4

normally distributed

Question 5

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

Answer 5

histrogram

Question 5

Random Sampling is virtually impossible

Answer 5

Volunteer sample

Snowball sampling

Purposive sampling

Convenience sampling

Question 6

We calculate the area under the curve, which will give
the number of people, which will give the probability of
the _____of responses.

Answer 6

range

Question 6

Most of us will never need to know the ________of
the normal curve.

Answer 6

exact equation

Question 6

Formula for Area of Triangle

Answer 6

W x H x 0.5

Question 6

under the curve is equal to the number of people

Answer 6

area

Question 7

There is a formula 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 ______

Answer 7

any range of responses.

Question 8

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

Answer 8

formula

Question 8

frequency of a given value of X*

Answer 8

big Y

Question 9

mean of the distribution

Answer 9

µ

Question 9

any score in the distribution

Answer 9

big X

Question 10

total frequency of the distribution

Answer 10

N

Question 11

a constant of 3.1416

Answer 11

π

Question 12

a constant of 2.7183

Answer 12

e

Question 13

The _______ goes on to infinity in each
direction.

Answer 13

Normal Distribution

Question 13

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 13

(Mean and
Standard Deviation)

Question 14

There is no beginning and end to the ______ on a normal
distribution plot, at least in theory.

Answer 14

x-axis

Question 14

In a normal distribution half of the ______will lie above
the mean and half below the mean.

Answer 14

scores

Question 15

This means we can use the area under the curve to find
the _______ of any value or range of values.

Answer 15

probability

Question 15

95.45% of cases lie within _____ of the Mean.

Answer 15

2 SDs

Question 16

47.72% of cases lie between the Mean and______

Answer 16

-2 SDs

Question 16

2.27% of cases lie

Answer 16

more than 2 SDs below the Mean

Question 16

49.9% of cases lie between the Mean and ____

Answer 16

+3 SDs

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 or standard score

Question 17

A z score is a transformed score that designates how
many Standard Deviation units the corresponding raw
score is ______

Answer 17

above or below the Mean.

Question 18

process by which the raw score is
altered is called a.

Answer 18

Score transformation

Question 19

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

Answer 19

z = score – mean / σ (standard deviation)

Question 20

The z transformation results in a distribution having a ____

Answer 20

Mean of 0 and an SD of 1.

Question 21

comparing scores that are not otherwise
directly comparable.

Answer 21

important use

Question 21

Z scores allow us to determine the ______ that fall above or below any score
in the distribution.

Answer 21

number or percentages of scores

Question 22

the ability to compare scores that are measured on
different scales is of fundamental importance to the topic of ______

Answer 22

correlation

Question 23

Z scores have the _____ as the set of raw scores.

Answer 23

same shape

Question 24

Transforming the ______ into their corresponding z
scores does not change the shape of the distribution.

Answer 24

raw scores

Question 25

The scores do not change their _________. All that
changes are the score values.

Answer 25

relative positions.

Question 26

The mean of the z scores always equals____

Answer 26

zero

Question 27

The scores
located at the mean of the raw scores will also be at the
________

Answer 27

mean of the z scores.

Question 28

The SD of z scores always equals to

Answer 28

1

Question 29

A raw score that is 1 SD above the mean has a z
score of

Answer 29

+1

Question 30

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 30

Sampling distribution of the mean

Question 31

With a smaller sample, the distribution will be

Answer 31

t-shaped

Question 32

Tells us that, given some assumptions, the sampling
distribution of the mean will form a normal distribution,
with a large sample.

Answer 32

Central Limit Theorem

Question 33

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

Answer 33

normal

Question 34

tells us that if the distribution in the sample is
approximately normal, then the sampling distribution
will be the correct shape

Answer 34

central limit theorem

Question 35

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

Answer 35

normal (or t-shaped).

Question 36

The larger the sample, the less we need to worry about
whether our sample data are

Answer 36

normally distributed or
not.

Question 36

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

Answer 36

central limit theorem

Question 37

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

Answer 37

requirements for accuracy

Question 37

How large is “large enough”?

Answer 37

depends on two factors

Question 38

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

Answer 38

The shape of the underlying population.

Question 39

some statisticians say that a sample size of 30
is large enough when the population distribution is
roughly _____

Answer 39

bell-shaped

Question 40

Others recommend a sample size of at least____

Answer 40

40

Question 41

But if the original population is distinctly not normal
(e.g., is badly skewed, has multiple peaks, and/or has
outliers), researchers like the sample size to be even_____

Answer 41

larger

Question 41

standard deviation of the
sampling distribution of the mean.

Answer 41

Standard Error ( se )

Question 42

The Standard Error should be affected by the_______ The bigger the sample, the closer our sample
mean is likely to be to the population mean.

Answer 42

Sample Size

Question 43

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 43

Amount of Variation in Sample