Essential Question: How does the US justice system
compare to statistical analysis? 
Hypothesis or Significance
Testing

State the question asked by a significance test
and the two possible answers. Is there clear
evidence of an effect?
 State a generic null
hypothesis.
There is no clear evidence of an
effect.
There is nothing new or out of the ordinary.
The status quo exists.
 State a generic alternative hypothesis.
There is
clear evidence of an effect.
 Give the null and alternative hypothesis for the American justice system.
Null Hypothesis: not guilty. This is the status quo for most people.
Alternative Hypothesis: guilty
 Define Pvalue.
Assuming Ho is true, the probability of
obtaining a test statistic as extreme or more extreme than the
one obtained is ______.
The smaller the
pvalue, the stronger the evidence is against Ho

State the statistic used for
indicating the level of significance. (Hint:
it begins with a "p".)

State the type of distribution used for tests of
significance. The sampling
distribution.

Describe one tail and two tail tests from the standpoint
of the null hypothesis and the pvalues.

Be as one
with "ztest for a population mean".

Perform "ztest for a population mean" in the following ways:

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

by hand, using the
calculator only for basic mathematics and finding areas

using the hypothesis testing features
of the TI83

using Minitab software
Homefun (formative/summative assessment):
Exercise 1, 5, 7, 9, 15, 17 pp. 546 to 547
Essential Question: Can a statistically significant
hypothesis have no practical value? 
Alpha Levels

Define
the significance level, alphapredetermined maximum acceptable pvalue
for rejecting the null hypothesis.
 Use one and two tailed tests of
significance.
onetailed: area
of tail = alpha
twotailed: area of each tail = (alpha) / 2

Use alpha to evaluate statistical
significance.

Use a confidence interval (confidence
level = C) as a
significance or hypothesis test.
significance level =
(1  C)
a
confidence interval is essentially identical to a 2tail
hypothesis test.
Formative Assessment: What two types of statistical tools are used for
inference and what type of distribution is used for making inferences?

Describe the difference between
statistical and practical significance. Even
a tiny difference between xbar of a sample and a population will be statistically significant if the sample size is large enough. Such a tiny difference may have no practical significance.

State when statistical inference is not
valid. (When based on data from a poorly
designed study or experiment.)


Homefun (formative/summative assessment):
Essential Question: How many ways can you
make an error of judgement? 
Types of
Errors
 Pass the ultimate test of
true statistics nerdhood: Explain the difference
between type 1 and type 2 errors.
 Explain what a type 1 and type 2 error is for the American justice system.
 Ho: innocent, Ha: guilty
 type I
error: punish an innocent person
 type 2
error: let a guilty person go free
 Explain what a type 1 and type 2
error is for quality control in manufacturing.
 Ho: the product is acceptable to the customer
 Ha: the product is unacceptable to the customer
 type I
error: reject acceptable product and don't ship it.
 type 2
error: ship unacceptable product to the customer

Generate a truth table for a hypothesis test.

State how alpha relates to the type 1 error. Whether a one or two tailed test, alpha always = type 1 error.

Name the hypothesis which is
considered true when determining the probability of having a type 1
error. H_{o}

Name the hypothesis which is considered true when
determining the probability of having having a type 2 error. H_{a}

Identify the areas representing the probabilities
of type 2 and type 1 errors on a diagram of a hypothesis test showing a
hypothetical sampling distribution.

Determine alpha and beta. beta = type 2 error
Power given: β = (1 
power)
Special
Cases for β = Type 2 Error 
μ_{Ha} = μ_{Ho}: β = (1  α) 
μ_{Ha} = (α boundary): β = 50% 

Determine the power of a hypothesis test. power = (1  β)
Beta
given: power = (1  β)
Special
Cases for Power 
μ_{Ha} = μ_{Ho}: power = α 
μ_{Ha} = (α boundary): power = 50% 

Plot and interpret a power curve
(power vs. separation between μ_{Ho} and μ_{Ha}) for a hypothesis
test.

sigmoidal shape

at zero separation power = alpha

asymptote at 100% (as separation
approaches infinity, power approaches 100%)

State how power can be applied to quality testing
in manufacturing.
Homefun (formative/summative assessment):
Exercise 21, 23, 25, 27, 29 pp. 548 to 549
Summative Assessment: Test Objectives 127
Essential Question: How does a confidence interval for
proportions compare to one for means? 
Ch. 12.1 Inference for Proportions

State the meaning of phat. A statistic estimating a population
proportion
phat = 
count of successes in sample 
count
of observations in sample 

Calculate the mean and standard deviation of a
binomial distribution.
Data Type 
Mean 
Std Dev 
count or number 
np 
[np(1  p)]^0.5 
proportion 
p 
[p(1  p) / n]^0.5 

Be aware that a binomial distribution (the
distribution typically used for analyzing proportions) is
essentially a sampling distribution. Note that as a sampling distribution, when the sample size is
large enough (see below), the distribution begins to resemble a
normal distribution.

When appropriate, correctly model a binomial
distribution as a normal distribution if the 2 conditions shown
below are met.
np ≥ 10
n(1p) ≥ 10 


Perform a hypothesis test
comparing a single large sample proportion (phat) against a know
population proportion (p). Note, this
is a one proportion ztest.
Z = 
(phat)  p 
[p(1p)/n]^{0.05} 
Homefun (formative/summative assessment): Exercise 35, 39, 41, 43, 47, 57, 59 pp. 562 to 565
Essential Question: How can we perform significance tests with small samples and an unknown standard deviation for the population? 
Estimating a Population Mean When Its Standard Deviation is Unknown

State the 2 assumptions that need to be met for using a ttest.

Calculate standard error
of a tstatistic
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 )

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):
