Download Point Estimates

12/4/2014
Remember…..
Population
It
Point Estimates
Sample
It
Parameter
Quantity computed from values in a
population
Usually
is the set of all objects being studied
is a subset of the population
Statistic
not known
Quantity computed from values in a
sample.
Computed
µ
σ
x
s
p
p
Point Estimate
It is a single number that is based on
sample data that represents a plausible
value of the characteristic for the
population.
It’s the statistic (from a sample) that we
use to estimate the parameter (of the
population).
directly from sample data
Examples
To find a point estimate of the average height of
students in this class I could use a sample of 10
people and find their average height.
To find the percent of green M&M’s in a bag, I
could use 20 bags and find the average percent
in those bags to estimate the true population
proportion.
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12/4/2014
An article on affirmative action reported that 537 of
the 1013 people surveyed believed that affirmative
action programs should be continued. Find a point
estimate of the population proportion.
Point estimate of p is:
૞૜ૠ
ෝ=
࢖
= ૙. ૞૜૙
૚૙૚૜
Based on the sample, we estimate that
53% believe that affirmative action should
continue.
Calories per ½ cup serving for 16 popular chocolate ice
cream is shown below. Find a point estimate for the
number of calories in a serving of chocolate ice cream.
Calories per ½ cup serving for 16 popular chocolate ice
cream is shown below. Find a point estimate for the
number of calories in a serving of chocolate ice cream.
270
170
160
160
199
160
150
180
150
140
160
290
190
170
110
170
Calories per ½ cup serving for 16 popular chocolate ice
cream is shown below. Find a point estimate for the
proportion that are greater than 190.
We could use the
270
170
160
160
199
160
150
180
150
140
160
290
190
170
110
170
mean:
median:
We tend to pick an estimate that
yields an accurate estimate.
To estimate a proportion – we use a proportion
(not a mean).
To estimate how many – we use the mean,
median, or trimmed mean
To estimate variation – we use standard
deviation, variance, or range
270
170
160
160
199
160
150
180
150
140
160
290
190
170
110
170
For our class (the population),
find a point estimate for the …
Average height
Difference between height of girls & height
of the boys
Proportion with brown eyes
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Unbiased Statistic
Examples of unbiased
estimators
It’s a statistic whose mean value is equal
to the value of the population being
estimated.
Biased – not equal to the population being
estimated.
median
trimmed mean
Biased: Range
If using a sample – it will only equal the
population if you have the lowest & highest
values. The probability for this to happen
is very small – almost 0.
Thus it’s biased because for most, the
sample range is smaller than the
population range.
mean: x
Proportion: ࢖
ෝ
Variance:
s2
∑ ( x − x)
=
n −1
2
∑x
=
2
−
(∑ x)
2
n
n −1
Airborne Times: 57, 54, 55, 51, 56, 48, 52,
51, 59, 59. Find point estimate of mean &
variance.
Put them in list 1
Do 1-var Stat
To get the variance, you must take the st.
dev. (Sx) and square it.
Homework
Page 481 (1-4, 25, 26)
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