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Sampling Analysis

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Sampling Analysis

Sampling Analysis

Statisticians collect information aboutspecific groups through surveys.

The entire group of objects or peoplethat you want information about in asurvey is called a population.

Sampling is a part of the populationthat we examine in order to gatherinformation about the entire population.

Sampling Analysis

If conclusions about a population are tobe valid, then the method used to choose the sample from the population must be sound.

Poor samples can lead to incorrectconclusions about a population

Random Sampling Method

A random sample is a sample that is chosen by chance. This gives all individuals in a population an equal chance to be selected.

Today most random sampling is done using computer software since the software can quickly select a specific number of names from a population.

Random Sampling Example

A random sample can be selected by putting the names of all the people in a population in a hat and then drawing a number of the names from the hat.

Stratified RandomSampling Method

A stratifiedrandom sample is a sample that first divides a population into groups of individuals that are similar in some way that is important to the survey.

Then it selects samples from each one of the groups and combines them to make up the actual sample.

Stratified Random Example

A college has 30,000 students, of whom 3,000 are graduate students.

Separate the students into graduate and undergraduate groups, and then select a sample of graduate students and a sample of undergraduate students.

These two samples make upthe stratified sample.

Systematic RandomSampling Method

A systematicrandom sample selects smaller groups within the populations in stages, resulting in a sample consisting of clusters of individuals.

For example, select a number n then survey every nth person.

Systematic Random Sample

You want to conduct a system at the local mall. You select the number 7. Then you survey every 7th personwho enters the mall.

This is an example ofsystematicrandom sample.

Biased Questions

When designing a survey, having a sample that represents the general population is very important. In addition, the questions in the survey must be worded carefully.

Biasedquestions make assumptions that may or may not be true. They also can make one answer choice seem better than another.

Experimental Probability

Objectives

Determine the experimental probability of an event.

Use experimental probability to make predictions.

An experiment is an activity involving chance. Each repetition or observation of an experiment is a trial, and each possible result is an outcome. The sample space of an experiment is the set of all possible outcomes.

Example 1: Identifying Sample Spaces and Outcomes

Identify the sample space and the outcome shown for each experiment.

A. Rolling a number cube

Sample space:{1, 2, 3, 4, 5, 6}

Outcome shown: 4

B. Spinning a spinner

Sample space:{red, green, orange, purple}

Outcome shown: green

Try 1

Identify the sample space and the outcome shown for the experiment: rolling a number cube.

Sample space: {1, 2, 3, 4, 5, 6}

Outcome shown: 3

An event is an outcome or set of outcomes in an experiment. Probability is the measure of how likely an event is to occur. Probabilities are written as fractions or decimals from 0 to 1, or as percents from 0% to 100%.

You can estimate the probability of an event by performing an experiment. The experimental probability of an event is the ratio of the number of times the event occurs to the number of trials. The more trials performed, the more accurate the estimate will be.

Example 3A: Finding Experimental Probability

An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of the event.

Spinner lands on orange

Example 3B: Finding Experimental Probability

An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of the event.

Spinner does not land on green

Try 3a

An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of each event.

Spinner lands on red

Try 3b

An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of each event.

Spinner does not land on red

You can use experimental probability to make predictions. A prediction is an estimate or guess about something that has not yet happened.

Example 4A: Quality Control Application

A manufacturer inspects 500 strollers and finds that 498 have no defects.

What is the experimental probability that a stroller chosen at random has no defects?

Find the experimental probability that a stroller has no defects.

= 99.6%

The experimental probability that a stroller has no defects is 99.6%.

Example 4B: Manufacturing Application

A manufacturer inspects 500 strollers and finds that 498 have no defects.

The manufacturer shipped 3500 strollers to a distribution center. Predict the number of strollers that are likely to have no defects.

Find 99.6% of 3500.

0.996(3500) = 3486

The prediction is that 3486 strollers will have no defects.

Try 4a

A manufacturer inspects 1500 electric toothbrush motors and finds 1497 have no defects.

What is the experimental probability that a motor chosen at random will have no defects?

Find the experimental probability that a motor has no defects.

= 99.8%

Try 4b

A manufacturer inspects 1500 electric toothbrush motors and finds 1497 have no defects.

There are 35,000 motors in a warehouse. Predict the number of motors that are likely to have no defects.

Find 99.8% of 35,000.

0.998(35000) = 34930

The prediction is that 34,930 motors will have no defects.