Imperfect Testing

Unit 7Lesson 1 and 2

Lesson One Part OneVocabulary Sample Representative

sample Population Percentage Pie chart

For large groups, surveying makes it easier to find a representative sample of a group. This is a group that would be similar to an entire group been studied.

Estimation

Sensitive Questioning Have you ever used an illegal drug? Because this a sensitive question

and because students themselves would be interested in each other’s answers, you probably could not guarantee to keep all responses confidential. Instead, ask a less sensitive questions.

Estimation Continued Approximate Probability Estimate Percentage Event Mutually Exclusive

Events Complementary

Events Scatter Plot

Events and Probability For many

experiments, some outcomes are more likely than others.

Event: an outcome or collection of outcomes

Probability: how likely a particular event is to occur.

TI 83 Simulation Set a seed number, a non-

zero number and store in rand.

Set the number of draws. Enter the portion of

population that has the trait that you are surveying.

This works for well when you have a huge number of draws. It would take a long time to simulate 500 draws or surveys by hand.

Mutual or Complementary? 8th Grader; 6th

Grader You can’t fit into both

categories, so this would be a mutually exclusive event.

8th grader and not an 8th grader.

When two mutually exclusive events combined comprise of an entire population, you get a complementary event

On One Condition

Vocabulary Variable Randomizing

Device Misleading

The Warner Model

The Warner Model of randomized response technique is used to get a more accurate answer to sensitive survey questions. This is a two stage process.

1st Stage: Select the statement

2nd Stage: Make sure the response is Yes or No

Probability and Events Vocabulary Conditional Probability Unconditional Probability Dependent Events Independent Events Tree Diagrams Glyph Diagrams Two-way table

Probability in an Event Unconditional Probability- Only fits into or

can answer in one way. Example: Student participates in after school

activities. Conditional Probability- Only fit into or can

answer only one way but there is a condition you have to answer. This will have a Yes/No answer.

Example: Student participates in after school activities and is a girl.

Two Way Table

Total

Total

Event One: Yes

Event One: No

Event Two: Yes Event Two: No

Tree Diagram

Total Population Stage One

Stage Two

Summary Probability represents the long-

term relative frequency of some event’s occurring. One way to estimate a probability is to count the number of successes in a set of trials. Sometimes different events in an experiment are related in some way. For example, think of some event. This event can either happen or not happen. That means that “not happen” is also an event, and it is clear that these two are related in two ways. First, “happen” and “not happen” cannot both occur on the same observation. These are complementary events.

Complementary events represent one possible relationship among events. Events may also be independent or mutually exclusive (which are not the same things).

There is a variety of representations prove useful in describing and working with related probabilities. Among these representations are tree diagrams, tables, and glyphs. Remember that every probability shown along a branch segment in a tree diagram is a conditional probability.