Normal distribution and statistical inference

Question 1

For normal distribution, what shape is the curve?

Answer 1

bell shaped

Question 2

what are the properties of normal distribution?

Answer 2

Question 3

what does this symbol mean in statistics?

Answer 3

mean

Question 4

what does this symbol mean in statistics?

Answer 4

standard deviation

Question 5

give examples of data that would occur in normal distribution

Answer 5

Question 6

for a normal distribution, it is bell shaped, but the shape/height of the bell depends on what?

Answer 6

standardization

Question 7

is this a distribution with a relatively smaller or larger standard deviation?

Answer 7

very small

Question 8

is this a distribution with a relatively smaller or larger standard deviation?

Answer 8

relatively larger

Question 9

is this a distribution with a relatively smaller or larger standard deviation?

Answer 9

large standard deviation

Question 10

the larger standard deviation a curve has, the more/ less? dispersion

Answer 10

more

Question 11

Properties of normal distribution

comment about the mean and standard deviation that it has

Answer 11

can have any mean or any standard deviation

Question 12

Properties of normal distribution

what 2 parameters is the normal distribution shape determined back?

Answer 12

mean and standard deviation

Question 13

1

Answer 13

A

Question 14

2

Answer 14

B

Question 15

which normal curve has the greatest mean?

Answer 15

B

Question 16

which normal curve has the greatest standard deviation?

Answer 16

C

Question 17

another normal distribution property is empirical rule

what does this say?

Answer 17

if our data is normally distributed, then around one standard deviation from either side of the mean, the curve will cover 68% of all observed data

Question 18

another normal distribution property is empirical rule

within 2 standard deviations from either side of the mean, the curve will cover how much % of the observed data?

Answer 18

95%

Question 19

another normal distribution property is empirical rule

within 3 standard deviations from either side of the mean, the curve will cover how much % of the observed data?

Answer 19

99.7%

Question 20

Answer 20

solution: draw the curve

therefore, answer is 95%

Question 21

Answer 21

Question 22

define population

Answer 22

Question 23

define sample

Answer 23

Question 24

define descriptive statistics

Answer 24

describe the data set, but doesn’t allow
us to draw any conclusions or make
any interferences about the data.

Question 25

define Inferential statistics

Answer 25

draw conclusions or
inferences about characteristics of
populations based on data from a
sample.

Question 26

what would the population parameter in this example be?

Answer 26

mean number of times a day that
children brush their teeth

Question 27

As in this example, It is clearly impractical so we select 50 school-aged children
in the UK and ask them how often they brush their teeth.

So, how do we gather the sample statistics?

Answer 27

the mean number of times these 50
children brushed their teeth (e.g. 1.7 times a day).

Then we might conclude:
School-aged children in the UK brush their teeth on average 1.7
times a day.

Question 28

therefore, what is statistical inference?

Answer 28

the process
of making an estimate, prediction, or decision
about a population based on a sample

Question 29

what is sample variation?

Answer 29

Statistics vary from sample to sample due to
random chance

Question 30

example of sample variation?

Answer 30

• A population of 100,000 people has an
  average IQ of 100 (If you actually could
  measure them all!)
• If you sample 5 random people from this
  population, what will you get?

Question 31

From this histogram from selected samples, which would be the average IQ score per sample?

Answer 31

the middle line

Question 32

sampling variation and sample size:

Do you expect more or less sampling variability
(SE) in samples of 10 people (than 5)?

Answer 32

sampling variation and sample size:

Do you expect more or less sampling variability
(SE) in samples of 10 people (than 5)?

Question 33

sampling variation and sample size:

Do you expect more or less sampling variability
(SE) in samples of 50 people (than 5)?

Answer 33

sampling variation and sample size:

Do you expect more or less sampling variability
(SE) in samples of 10 people (than 5)?

Question 34

sampling variation and sample size:

Do you expect more or less sampling variability
(SE) in samples of 100,000 people (than 5)?

Answer 34

the larger of people you have, the more accurate it is, so less sampling variation

Question 35

define standard error

Answer 35

Standard Error is a measure of sampling
variability

Standard error is the standard deviation of
a sample statistic.

Question 36

Standard error …….. with increasing
sample size

Answer 36

decreases

Question 37

Standard error ……… with increasing
variability of the outcome.

Answer 37

increases

Question 38

what is the formula for a confidence interval?

Answer 38

Question 39

what is the 95% confidence interval for the mean IMD score?

Answer 39