Normal distribution and statistical inference Flashcards
For normal distribution, what shape is the curve?
bell shaped
what are the properties of normal distribution?
what does this symbol mean in statistics?
mean
what does this symbol mean in statistics?
standard deviation
give examples of data that would occur in normal distribution
for a normal distribution, it is bell shaped, but the shape/height of the bell depends on what?
standardization
is this a distribution with a relatively smaller or larger standard deviation?
very small
is this a distribution with a relatively smaller or larger standard deviation?
relatively larger
is this a distribution with a relatively smaller or larger standard deviation?
large standard deviation
the larger standard deviation a curve has, the more/ less? dispersion
more
Properties of normal distribution
comment about the mean and standard deviation that it has
can have any mean or any standard deviation
Properties of normal distribution
what 2 parameters is the normal distribution shape determined back?
mean and standard deviation
1
A
2
B
which normal curve has the greatest mean?
B
which normal curve has the greatest standard deviation?
C
another normal distribution property is empirical rule
what does this say?
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
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?
95%
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?
99.7%
solution: draw the curve
therefore, answer is 95%
define population
define sample
define descriptive statistics
describe the data set, but doesn’t allow
us to draw any conclusions or make
any interferences about the data.
define Inferential statistics
draw conclusions or
inferences about characteristics of
populations based on data from a
sample.
what would the population parameter in this example be?
mean number of times a day that
children brush their teeth
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?
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.
therefore, what is statistical inference?
the process
of making an estimate, prediction, or decision
about a population based on a sample
what is sample variation?
Statistics vary from sample to sample due to
random chance
example of sample variation?
- 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?
From this histogram from selected samples, which would be the average IQ score per sample?
the middle line
sampling variation and sample size:
Do you expect more or less sampling variability
(SE) in samples of 10 people (than 5)?
sampling variation and sample size:
Do you expect more or less sampling variability
(SE) in samples of 10 people (than 5)?
sampling variation and sample size:
Do you expect more or less sampling variability
(SE) in samples of 50 people (than 5)?
sampling variation and sample size:
Do you expect more or less sampling variability
(SE) in samples of 10 people (than 5)?
sampling variation and sample size:
Do you expect more or less sampling variability
(SE) in samples of 100,000 people (than 5)?
the larger of people you have, the more accurate it is, so less sampling variation
define standard error
Standard Error is a measure of sampling
variability
Standard error is the standard deviation of
a sample statistic.
Standard error …….. with increasing
sample size
decreases
Standard error ……… with increasing
variability of the outcome.
increases
what is the formula for a confidence interval?
what is the 95% confidence interval for the mean IMD score?
