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T7_Interpretations_and_Central_Limit_Theorem_Upload.pptx
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T7 Interpretations and Central Limit Theorem Uplo...
T7_Interpretations_and_Central_Limit_Theorem_Upload.pptxStatistics Through Example STA 1013 Lexi
T7 Interpretations and Central Lim...
T7_Interpretations_and_Central_Limit_Theorem_Upload.pptxStatistics Through Example STA 1013 Lexi
Page 11
Interpretation
Zscore
Z = 0.72
Interpretation
Since the zscore is negative, the data value
of 67 inches is located 0.72 standard
deviations below the mean of 69.1 inches.
ZTable to Density Curve
p = 0.2358
The area under the curve is 0.2358.
Data Interpretation
About
23.6%
of the time we expect to see
males shorter than 67 inches.
Adjusted wording
If the mean height in inches for a male is 69.1 inches and the standard deviation is 2.9 inches, what
percent
of males are shorter than 67 inches?
Page 12
Interpretation
If the mean height in inches for a
male is 69.1 inches and the
standard deviation is 2.9 inches.
Write out in words, in context
, what
the shaded area in the picture
below represents.
Page 13
Interpretation
If the mean height in inches for a
male is 69.1 inches and the
standard deviation is 2.9 inches.
Write out in words, in context
, what
the shaded area in the picture
below represents.
Page 14
Central Limit Theorem
Page 15
Central Limit Theorem
Until this point, we’ve worked with the distribution of a sample of
individual
observations
●
This is every observation in the sample plotted individually on
the curve
●
We got a sense of how spread out our data is and we can also
calculate the probability of getting an observation in a certain
range
○ Example:
for a population, the mean height = 69 in. with SD
= 1 in. What is the probability I randomly choose someone
within 1 inch of the mean?
Kelly Findley, Florida State
University
Page 16
Central Limit Theorem
Let us now take
multiple
samples, or many simple random samples, of
size n for a variable with any distribution (not necessarily a normal
distribution) and record the mean of each sample. We now have a
.
.
1. The
distribution of means
will approximately be a normal
distribution for
.
sample sizes.
2.
The mean of the
distribution of means
approaches the
.
mean,
, for large sample sizes.
3.
The standard deviation of the
.
approaches
/√n
, for large sample sizes, where
is the
standard deviation of the population.
Page 17
Central Limit Theorem
Let’s take
multiple
samples, or many
simple random
samples, of size n for
a variable with any
distribution
Example Let’s look at the
distribution for the length
of strawberries.
Page 18
Central Limit Theorem
1. The
distribution of
means
will
approximately be a
normal distribution
for large sample
sizes.
What does this mean?
Of the _____
.
samples that
we took of size 30, ﬁnd
the mean length of a
strawberry for every
sample.
Using these ____________
.
,
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