Essential Question:
How can you express a measurement
in an internationally accepted manner? 
Confidence Intervals

State the 3 parts of
a confidence interval and explain their meaning.
Confidence level 
the fraction or
percentage of conf. intervals that will contain the
parameter in a large number of trials (see drawing at right) 
Estimate 
the statistic
used to estimate a parameter, often a sample mean 
Margin
of error 
2*(ME) = (width
of conf. int ) 

State the type of
distribution which confidence intervals (CIs) are based on and explain what characteristic makes it so useful.CIs are based on sampling
distribution, which given a large enough sample size, tend to be normally distributed. This is a great advantage because the mathematics of normal distributions are well defined.

Sketch
the appropriate picture of a confidence interval. A confidence interval is always represented as a symetrical center section of a normal distribution representing the sampling distribution. See the blue distributions shown at right.

Calculate margin of error when standard
deviation is known.
ME = z^{*} [σ_{p} / (n)^{0.5}]

Describe what
happens to the margin of error as confidence level (C) is increased.



Formally state the
meaning of a level C confidence interval. If a study were repeated numerous times, C represents the expected % of the resulting confidence intervals that would contain the true parameter.

Tell why the margin
of error is not a measure of accuracy in the data.

The
accuracy of a estimate is typically unknown.
(Remember,
we would have to know the true parameter to determine the accuracy of
the estimate because accuracy is a measure of how close an extimate comes to the true parameter.)

ME
depends on an arbitrarily determined value of C.
(C usually = 95% but this is a
convention not a mathematically derived principle

Given that margin of
error is not a measure of accuracy or "error," State what it
really represents.
(Expected
sampling variability)

Be as one with the
cautions.
Homefun
(formative/summative assessment):
Exercise 5, 9, 17, 21, 23, 25, pp. 480 to 484
Essential Question: How does a confidence interval for
proportions compare to one for means? 
Inference for Proportions

State the meaning of p and p̂, phat.
 State the standard deviation of the sampling distribution (SD)
σ_{p̂} = [ p (1  p ) / n ]^{0.5}

Create a large sample confidence
level for a proportion. Since p is not known p̂ must be used instead for calculating standard error, an estimate of the standard deviation of the sampling distribution.
Confidence Interval = p̂ ± z^{*} [ p̂ (1  p̂ ) / n ]^{0.5}
Requirements:
Normally Distributed SD: np >= 10 and n(1  p) >= 10
Population Size >= 10n

Given a target value for the maximum acceptable margin of error, calculate the minimum sample size.Hint: When the true proportion is not known always use p̂ = 0.5 or 50%. This give the most conservative value for n when solving for n using the following equation:
ME = z^{*} [ p̂ (1  p̂ ) / n ]^{0.5}
Homefun (formative/summative assessment): Read section 8.2  Exercises 29, 35, 39, 41, 43, 45, 51, pp. 496  498
Essential Question: How can we account for the greater
uncertainty of analyzing data when sample size is small and little
is known about the population? 
Estimating a Population Mean When Its Standard Deviation is Unknown

State the 2 assumptions for drawing inferences
about a population mean when sigma is not known.

Calculate standard error
of a statistic
SE = s / ( n^.5 ) .

If the sample size is large, the zinterval can be used with the above SE.
 Explain when a t statistic is used rather than
a zscore.
 Population Standard deviation not known
 Sample Size is Small

Calculate t statistics.

State the degrees of freedom for a onesample ttest. df = ( n1 )

Construct confidence intervals using the t statistic.
ME = t^{*} s / ( n^{0.5 })

Perform one sample tprocedures:

by hand (using the
calculator only for basic mathematics) using ttables.

by hand, using the
calculator only for basic mathematics and finding areas.
 tcdf (L,U,D)
 Lower tvalue
 Upper t value
 Degrees
of Freedom
μ is the mean associated with H_{a}
μ_{o} is the mean associated with H_{o}
 Use the tdistribution with the following limitations:
Sample Size 
Skew 
Nearly NDistr 
Outliers 
Less than 15 
None 
Yes 
No 
At least 15 
Minor 
Yes, minor skew ok 
No 
At least 30 
Significant 
Yes, skew ok 
No 
Homefun
(formative/summative assessment): Read section 8.3, Do Exercises 55, 59, 63, 69, 75, 77
Essential Question: How can I make an
"A" on the test? 
Confidence Interval
Review
 Master the vocabulary
 Work the practice test.
 Review the objectives.
Summative Assessment:
Unit Exam objectives 1  24
