|
|
Latin
|
Latin/Greek Root Words
|
|
|
(Statistics
connection) |
|
AP Statistics Standards
IV. Statistical Inference: Estimating
population parameters and testing hypotheses (30% –40%)
Statistical inference guides the selection of appropriate models.
A. Estimation (point
estimators and confidence intervals)
-
Estimating population
parameters and margins of error
-
Properties of point estimators,
including unbiasedness and variability
-
Logic of confidence intervals,
meaning of confidence level and confidence intervals, and properties of
confidence intervals
-
Large sample confidence
interval for a proportion
-
Large sample confidence
interval for a difference between two proportions
-
Confidence interval for a mean
-
Confidence interval for a
difference between two means (unpaired and paired)
|
|
|
| Essential Question:
Is there a way to get any
researcher in the world to agree agree that your conclusions are
reasonable even if they disagree with them? |
Ch 10.1 Statistical Inference
-
Correctly use the
term statistical inference.
To draw a conclusion from
data in a formal manner using well defined procedures
-
Give the quick and
dirty explanation of a confidence interval.
An estimate of a parameter based on a statistic accounting for
uncertainty.
Homefun: --
Read section 10.1
|
|
|
|
- Lesson 1
- Key Concept:
Statistical inference
- Purpose:
Gain an intuitive understanding of what
statistical inference is.
Stats Investigation (Teams of
two):
Interactive Discussion:
Objectives 1-2. What two things does a confidence interval give? Resources/Materials: two
decks of cards |
|
|
Stats
Investigation 10.1:
Estimating a Proportion |
| Purpose:
Determine a reasonable way to estimate a
proportion for a population. Instructions:
Write a rational hypothesis for what the proportion of red
cards is in a deck of cards.
Draw 10 samples with n=2 and 10
samples with n=20 from a deck of cards. Remove a card one at a
time. Replace and shuffle the deck each time a card is drawn.
Do this twice for each sample of two and twenty times for each
sample of 20. Record the the proportion of red cards for each
sample.
Create an interval around each
sample which you feel has a high chance of containing the
mean. Record your reasons for making the interval. Make two
plots of all the intervals. One for n=2 and one for n=20. The
plots should look like the one on page 511 minus the normal
distribution picture.
Repeat the process for a second
deck of cards.
Questions /Conclusions:
- Which sample size tended to
have the widest interval?
- Did every interval contain
the true mean?
|
|
| Essential Question:
How can you express a measurement
in an internationally accepted manner? |
Ch 10.1 Confidence Intervals
-
State the type of
distribution which confidence intervals are based on and sketch
the appropriate picture of a confidence interval.
-
State the 3 parts of
a confidence interval and explain their meaning.
Confidence level
Estimate
Margin of error
-
Describe what
happens to the margin of error as confidence level is increased.
-
Formally state the
meaning of a level C confidence interval. (magic box p. 514)
-
Tell why the margin
of error is not a measure of inaccuracy in the data.
-
State which form of
error a margin of error represents.
Sampling Error
-
Be as one with the
cautions listed on page 524.
Homefun: 10.1, 10.3,
10.9, 10.11, --
|
|
- Lesson 2
- Key Concept:
Confidence intervals
- Purpose:
Gain an intuitive understanding of what a
confidence interval is and how it gives more information than
just an estimate.
Interactive Discussion:
Objectives.
|
|
|
Stats
Investigation 10.2: Margin
of Error
|
| Purpose:
Determine the effects that changes in
confidence level, sample size, and standard deviation have on
margin of error. Instructions:
You will make three different plots as follows:
- Margin of error vs
confidence level with sigma = 1 and n = 100. Vary
confidence level from 60% to 99%.
- Margin of error vs sigma
with confidence level = 95%, and n = 100. Vary sigma from
1 to 5.
- Margin of error vs sample
size with confidence level = 95% and sigma = 1. Vary n
from 100 to 500.
Questions /Conclusions:
- What is the effect of
doubling the sigma and why?
- What is the effect of
doubling the sample size and why?
- What is the effect of
increasing the confidence level from 90% to 95%?
- Of the three items mentioned
above, which one(s) are under the control of the
experimenter?
- What type of error does the
margin of error represent?
- Why is margin of error not a
measure of accuracy?
- What sampling technique must
be used if valid confidence intervals are calculated?
- Is a high confidence level
necessarily more meaningful than a low confidence level?
|
|
AP Statistics Standards
IV. Statistical Inference: Confirming
models (continued)
B. Tests of significance
- Logic of significance testing, null
and alternative hypotheses; p-values;
one- and two-sided tests; concepts of Type I and Type
II errors; concept of power
- Large sample test for a proportion
- Large sample test for a mean
|
| Essential Question:
How does the US justice system
compare to statistical analysis? |
Ch 10.2 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 evidence of an effect.)
-
State a generic alternative hypothesis.
(There
is clear evidence of an effect.)
-
Give the null and alternative hypothesis for the
American justice system.
-
Define P-value.
-
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.
-
Describe one tail and two tail tests from the standpoint
of the null hypothesis and the p-values.
-
Be as one
with "z-test for a population mean" on page 546
-
Perform
"z-test for a population mean" in the following ways:
-
by hand (using the
calculator only for basic mathematics) using z-tables.
-
by hand, using the
calculator only for basic mathematics and finding areas
-
using the hypothesis testing features
of the TI-83
-
using Minitab software
Homefun: 10.29
- 10.32, 10.35, 10.37
|
|
|
Lesson 3
Key Concept:
Significance Testing or Hypothesis Testing
Purpose: Learn the format
for one of the key inference tools in statistics by comparing
them to the U.S. justice system.
Interactive Discussion:
Objectives.
p-value definition:
The
probability of obtaining a test statistic as extreme or more
extreme than the one obtained, assuming the null hypothesis is
true.
Why is the null hypothesis rejected when
the p-value is low?
How do the odds of correctly rejecting the null
hypothesis compare to the odds of winning money in Las Vegas?
Can a good hypothesis test compensate for a
faulty design of the system for collecting data?
What does a faulty design of a data collection
system do to the probability of being right?
|
|
| Essential Question:
Can a statistically significant
hypothesis have no practical value? |
Ch 10.2 Alpha Levels
-
Define statistical significance in terms of alpha.
-
Use one and two tailed tests of
significance.
-
Use alpha to evaluate statistical
significance.(p.542)
-
Use a confidence interval for a
significance test.
-
Describe the difference between
statistical and practical significance.
-
State when statistical inference is not
valid.
Homefun: 10.45,
10.53, 10.55 |
|
|
Lesson 4
Key Concept: Statistical
standards of judgment
Purpose: learn how to use
alpha levels in hypothesis tests.
Interactive Discussion:
Objectives
|
|
| Essential Question:
How many ways can you be wrong? |
Ch 10.3 - 10.4 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.
- Generate a truth table for a hypothesis test.
- State how alpha relates to the type 1 error.
- Name the hypothesis which is considered true when
calculating alpha.
- Name the hypothesis which is considered true when
calculating beta.
- 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.
- Calculate alpha and beta.
-
Calculate the power of a hypothesis test.
-
Plot and interpret a power curve for a hypothesis
test.
-
State how power can be applied to quality testing
in manufacturing.
Homefun: 10.67,
10.69,
10.71 |
|
|
Lesson 5
Key Concept: Type I and
type II errors, power of the test
Purpose: develop an
intuition for the elements that affect the above.
Interactive Discussion:
Objectives. Web Page Resource:
Type I and II Errors-Making Mistakes in the Justice System
.Use the applet provided to simulate various types of errors |
|