are examples of point estimates

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are examples of point estimates
Point estimates are comprised of a single number
obtained from data. A down side of a using a
point estimates is that there is no measure of
precision associated with them. An interval
estimate uses the information based on the
sampling distribution of the point estimate to
proved an interval on which the true parameter is
likely to reside. A wide interval denotes a less
precise estimate and a narrow interval denotes
more precision.
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Point estimate Margin of error
A cut-off value based on the degree of confidence
and the distribution of the point estimate
The standard error of the point estimate
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Confidence interval for a mean when the variance
is assumed to be known
Point estimate
Standard error of the point estimate
Cut-off value
Note z1-a/2 P(Zltz) 1-a/2 (1 a) is the
level of confidence Typical values of a are
0.1, 0.05, 0.01
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Assumes s is known (or n very large)
CI for a mean
CI for a proportion
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As confidence goes up, precision goes down
(intervals widen) Confidence a 1 - a/2 z1 - a/2
90 0.1 0.95 1.64 95 0.05 0.975 1.96
98 0.02 0.99 2.33 99 0.01 0.995 2.58
As sample size increases, precision increases
(intervals narrow)
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A random sample of 12 graduates of a certain
secretarial school typed an average of 79.3 words
per minute. Assume the standard deviation is 7.5
words per minute. Find a 95 confidence interval
for the mean number of words per minute.
We are 95 confident that the true mean typing
time is between 75.06 and 83.54 words per minute.
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A random sample of 12 graduates of a certain
secretarial school typed an average of 79.3 words
per minute with a standard deviation of 7.8 words
per minute. Find a 95 confidence interval for
the mean number of words per minute.
We are 95 confident that the true mean typing
time is between 74.34 and 84.26 words per minute.
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CBS News conducted its own poll of uncommitted
voters and found that Barack Obama won the third
debate by a wide margin 53 believed that Sen.
Obama was stronger. Suppose 400 voters were
polled. Find a 98 confidence interval for the
proportion of uncommitted voters that think
Barack Obama won the debate
We are 98 confident that the true proportion of
uncommitted voters than think Barrack Obama won
the third debate is between 47.2 and 58.5 .
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http//news.yahoo.com/s/ap/20080927/ap_on_el_pr/pr
esidential_debate_polls The CNN poll involved
telephone interviews with 524 adults who watched
the debate and had a margin of error of plus or
minus 4.5 percentage points. The CBS survey
involved online interviews with 483 uncommitted
voters who saw the debate and had an error margin
of plus or minus 4 points. It was conducted by
Knowledge Networks, which initially selected the
respondents by telephone. What was the
confidence level?