Apr. 7 Statistic for the day: Average number of handstands an adult male panda does each day: 8

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Apr. 7 Statistic for the dayAverage number of
handstands an adult male panda does each day 8
Source Harpers index

• Assignment
• Solve practice problems WITHOUT
• looking at the answers.

These slides were created by Tom Hettmansperger
and in some cases modified by David Hunter
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First, some data Change is good?
Questions 1. Do PSU women carry more change
than men? 2. Is there a greater proportion of
women who carry change than men?
Data from class, with outlier excluded
Sample Size Proportion carrying change Mean amount of change
Men 21 5/21 or 23.8 10.7 cents
Women 34 17/34 or 50.0 39.7 cents
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Confidence intervals Main exam topic

• Difference between population values and sample
  estimates
• Rules of sample proportions and sample means
• The logic of confidence intervals (what does the
  confidence coefficient mean?)
• SD for proportions, SE for means, and SD for
  differences between means
• How to create CIs for (a) one proportion (b)
  one mean (c) the difference of two means.
• Different levels of confidence

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Difference between population values and sample
estimates
A population value is some number (usually
unknowable) associated with a population. A
sample estimate is the corresponding number
computed for a sample from that population.
Examples include population proportion vs.
sample proportion population mean vs. sample
mean population SD vs. sample SD
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Rule of sample proportions
IF

1. There is a population proportion of interest
2. We have a random sample from the population
3. The sample is large enough so that we will see at
   least five of both possible outcomes

THEN

• If numerous samples of the same size are taken
  and the sample proportion is computed every time,
  the resulting histogram will
• be roughly bell-shaped
• have mean equal to the true population proportion
• have standard deviation estimated by

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Rule of sample means
IF

1. The population of measurements of interest is
   bell-shaped, OR
2. A large sample (at least 30) is taken.

THEN

• If numerous samples of the same size are taken
  and the sample mean is computed every time, the
  resulting histogram will
• be roughly bell-shaped
• have mean equal to the true population mean
• have standard deviation estimated by

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The logic of confidence intervals
What does a 95 confidence interval tell us?
(Whats the correct way to interpret it?)
IF (hypothetically) we were to repeat the
experiment many times, generating many 95 CIs
in the same way, then 95 of these intervals
would contain the true population value. Note
The population value does not move the
hypothetical repeated confidence intervals do.
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SD for sample proportions
The standard deviation of the sample proportion
is estimated by
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SE for sample means
The standard deviation of the sample mean is
estimated by
This estimate of the SD is called the STANDARD
ERROR OF THE MEAN, or sometimes SE mean or SEM.
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SD for difference between means
The standard deviation of the difference between
two sample means is estimated by
(To remember this, think of the Pythagorean
theorem.)
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How to create 95 CIs for

1. A population proportion
2. A population mean
3. The difference between two population means

Sample proportion 2(SD of sample proportion)
Sample mean 2(SE mean)
Diff of sample means 2(SD of diff of sample
means)
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Different levels of confidence

1. A population proportion
2. A population mean
3. The difference between two population means

Sample proportion 2(SD of sample proportion)
Sample mean 2(SE mean)
Diff of sample means 2(SD of diff of sample
means)
Replace the 2s with another number from p. 137!
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Example 90 confidence interval
Since 90 is in the middle, there is 5 in either
end. So find z for .05 and z for .95. We get z
1.64
90 confidence interval sample estimate
1.64(Std Dev)