Download C.5 Notetaking Guide - Mrs. McDonald

Name:
AP Statistics
C.5
Producing Data
5.1 Designing Samples – Notetaking Guide
Observational Study:
Experiment:
Population:
Sample:
Census:
Sample Design - Random
Simple Random Sample:
Ways to get a SRS.
Systematic Sample:
Stratified Random Sample:
Multistage Sampling:
Cluster Sample:
Sources of Bias
Bias:
Sample Design – Not Random
Voluntary Response Sample:
Convenience Sample:
Nonresponse:
Wording Effect:
Other Types of Bias.
Undercoverage:
Response Bias:
Using the Random Digits Table
A corporation employs 2000 male and 500 female engineers. A stratified random sample of 200 male
and 50 female engineers gives each engineer 1 chance in 10 to be chosen. This sample design gives
every individual in the population the same chance to be chosen for the sample.
Is it a SRS? Explain your answer.
Beginning with line 108 on the Random Number Table, reproduced below, select the first 5 female
engineers to be in the sample.
5.2 Designing Experiments – Notetaking Guide
Terms and Concepts:
Explanatory Variables
Response Variables
Experimental Units
Treatments
Subjects
Factors
Levels
Example: Over a 4-month period, among 30 people with bipolar disorder, patients who were given a
high dose of omega-3 fatty acids from fish oil improved more than those given a placebo.
Experimental Units
Treatments
Factors
Levels
Response Variable
Example: Scientists examined the glycogen content of rats’ brains at the rats’ normal bedtimes and
after they had been kept awake for an extra 6, 12, or 24 hours. The scientists found that glycogen
was 38% lower among rats that had been sleep-deprived for 12 hours or more, and that the levels
recovered during subsequent sleep. These researchers speculate that we may need to sleep in order
to restore the brain's energy fuel
Experimental Units
Treatments
Factors
Levels
Response Variable
Example: In this hypothetical experiment, the researcher is studying the possible effects of Vitamin
C and Vitamin E on health. The Vitamin C has three doses - 0 mg per day, 250 mg per day, and 500
mg per day. The Vitamin E has 2 doses - 0 mg per day and 400 mg per day.
Experimental Units
Treatments
Factors
Levels
Response Variable
Experimental Design
Three Important Characteristics of an Experiment:
Control:
Randomization:
Replication:
How to Control:
Control group:
Blinding:
Placebo:
Double Blind:
Placebo Effect:
Completely Randomized Design:
Example: Design a randomized experiment for this situation. Acme Medicine is conducting an
experiment to test a new vaccine, developed to immunize people against the common cold. To test the vaccine,
Acme has 1000 volunteers - 500 men and 500 women. The participants range in age from 21 to 70.
When are things said to be statistically significant?
Block Design vs. Matched-Pairs Design
Block Design:
Matched-Pairs Design:
Examples
We know that a medication has a greater effect
A study is conducted to see how effective aspirin
on men than on women…this would be a
is in reducing temperature in children. A sample
confounding variable. Control for that by
of 7 children suffering from influenza had their
grouping men together and women together and temperatures taken immediately before and 1
then comparing the results of a drug treatment.
hour after administration of aspirin. The results
are given below. We would like to conduct a
paired differences t-test for this situation. The
data follow.
Examples. Decide what type of design is needed.
Suppose a doctor wants to compare the anxiety-controlling drug currently on the
market with two new drugs. A group of patients from a local clinic is available for the
experiment. All three drugs are known to have different effects on men and women.
Design an experiment to compare the effects of the three drugs.
A local sickle-cell association offers programs to educate people about sickle-cell
anemia. The director of the association is interested in assessing the program’s effect
on the participants’ knowledge about the disease. Design an experiment to assess the
effectiveness of this educational progress.
A pharmaceutical company wishes to test a new medication it thinks will reduce
cholesterol. A group of 20 volunteers is formed and each has his or her cholesterol
measured. After 6 months the volunteers’ cholesterol is measured again and any
change from the beginning of the experiment is noted. The researcher believes the
initial cholesterol level may influence the change in cholesterol level. Create a design
that takes account of subjects’ initial cholesterol level.
5.3 Simulations – Notetaking Guide
Three ways to answer questions involving chance:
How to Perform a Simulation:
1.
2.
3.
4.
5.
Example of digit assigning:
70% of people are employed. You are going to SIMULATE a sample of size 18 to look at
unemployment rates.
How could you assign the digits?
Example 1:
Orders of frozen yogurt flavors have the following relative frequencies: 38% chocolate, 42% vanilla,
and 20% strawberry. We wish to simulate 10 frozen yogurt sales based on recent history.
What are we going to do?
What can we assume?
Assign digits:
Complete 10 TRIALS of 10 sales?
Analysis:
67642
05204
30697
44806
96989
68403
85621
45556
35434
09532
64041
99011
14610
40273
09482
62864
01573
82274
81446
32477
17048
94523
97444
59904
16936
39384
97551
09620
63932
03091
93039
89416
52795
10631
09728
68202
20963
02477
55494
39563
Example 2:
Suppose you take a true-false quiz and guess four answers at random. What is an experimental
probability that you will get at least three correct answers?
What are we going to do?
What can we assume?
Assign digits:
Perform the simulation - 10 TRIALS
40779
86382
48454
65269
91239
45989
45389
54847
77919
41105
43216
12608
18167
84631
94058
82458
15139
76856
86019
47928
96167
64375
74108
93643
09204
98855
59051
56492
11933
64958
Analysis:
Calculator procedure for the same problem.
Example 3:
A couple plans to have children until they have a girl or until they have four children, whichever
comes first. Perform a simulation to estimate the likelihood they will have a girl.
What are we going to do?
What can we assume?
Assign digits:
Perform the simulation - 20 TRIALS
65285
97198
12138
53010
94601
15838
16805
61004
43516
17020
17264
57327
38224
29301
31381
38109
34976
65692
98566
29550
95639
99754
31199
92558
68368
04985
51092
37780
40261
14479
Analysis:
Calculator procedure for the same problem.
Just for grins and giggles: What is the average number of boys that the couple might have?