Transcript Point Estimates

Point Estimates
Let’s explore

Find a point estimate of the area of the
rectangles on the page.
 How
many should we sample?
 Use Math – PRB – RandInt(1,100, n)
Questions

Do all of your trials contain the true mean of 7.4?
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What’s the shape of the graph?
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If mean is 7.4 and standard deviation is 5.126 ,
what is the mean & standard deviation of the
sampling distribution?
Point Estimate
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It is a single number that is based on
sample data that represents a plausible
value of the characteristic for the
population.
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It’s the statistic (from a sample) that we
use to estimate the parameter (of the
population).
Examples
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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.
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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.
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.
537
p
 0.530
1013
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Point estimate of p is:
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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.
270
170
160
160
199
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180
150
140
160
290
190
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170
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.
We could use the
270
170
160
160
199
160
150
180
150
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160
290
190
170
110
170
mean:
median:
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.
270
170
160
160
199
160
150
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150
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290
190
170
110
170
We tend to pick an estimate that
yields an accurate estimate.
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To estimate a proportion – we use a proportion
(not a mean).
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To estimate how many – we use the mean,
median, or trimmed mean
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To estimate variation – we use standard
deviation, variance, or range
For our class (the population),
find a point estimate for the …
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Average height
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Difference between height of girls & height
of the boys
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Proportion with brown eyes
Unbiased Statistic
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It’s a statistic whose mean value is equal
to the value of the population being
estimated.
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Biased – not equal to the population being
estimated.
Examples of unbiased
estimators
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mean: x
median
trimmed mean
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Proportion: p
Variance:
s2
x  x



n 1
2

x
2
x



n 1
n
2
Biased: Range
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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.
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Thus it’s biased because for most, the
sample range is smaller than the
population range.
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.
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Homework
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Page 481 (1-4, 25, 26)