Download population - Penn State Department of Statistics

Statistics
The big picture ...
Populations
• We want to learn about a population.
• A population is any large collection of objects
or individuals, such as people, students, or
trees about which information is desired.
• e.g. the heights of all Americans are: 74”, 58”,
72”, 65”, 68”, 71”, 71”, 69”, 63”, 63”, 66”, …
• e.g. the opinions of all college students about
marijuana use is: Y, N, N, Y, Y, Y, N, Y, ...
Parameters
• A population of measurements is too large
to collect and too large to say anything
meaningful about the population.
• A parameter is any summary number, like
an average or proportion, that describes the
entire population.
Parameters
• Examples include:
– population mean 
– population standard deviation 
– population proportion p
• 99.999999999999….% of the time, we
don’t (...or can’t) know the real value of a
population parameter. It is unknown!
• Best we can do is estimate the parameter!
Samples
• A sample is a representative group drawn
from the population.
• e.g. the heights of 10 Americans are: 74”,
58”, 72”, 65”, 68”, 71”, 71”, 69”, 63”, 66”
• e.g. the opinions of 20 college students
about marijuana use is: Y, N, N, Y, Y, Y, N,
Y, Y, Y, N, N, N, N, Y, N, N, Y, N, N
Statistics
• Because samples are manageable in size, we
can determine the value of statistics.
• A statistic is any summary number, like an
average or proportion, that describes the
sample.
Statistics
• Examples include:
– sample mean 
– sample standard deviation s
– the sample proportion (“p-hat”)
p̂
• We use the known statistic to estimate the
unknown parameter.
Which parameter?
Which statistic?
• The type of data collected determines:
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the appropriate parameter,
the appropriate statistic,
the appropriate confidence interval,
and the appropriate hypothesis test.
• Proportions summarize categorical data.
• Means summarize numerical data.
Two ways to learn
about a population parameter
• Confidence intervals estimate parameters.
– We can be 95% confident that the proportion of
Penn State students who have a tattoo is between
5.1% and 15.3%.
• Hypothesis tests test the value of parameters.
– There is enough statistical evidence to conclude
that the mean GPA of all Penn State science
majors is greater than 3.0.
Is our class representative of PSU
pop’n with respect to gender?
• Note that 55% of Penn State students are
female.
• Conduct hypothesis test:
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Specify hypotheses.
Collect sample data.
Define and determine P-value.
Make decision and draw conclusion.
Acknowledge possible errors.
Does data suggest that two cars A
and B handle differently?
• The two cars have different lengths, wheel
bases, and turning radii.
• Experiment conducted on 14 subjects.
• Measurements are time in seconds required
for subjects to parallel park each car.
• Hypothesis test conducted. Results reported
in paper “Relative Controllability of Dissimilar
Cars,” in journal Human Factors, 1962.