how do i study different sampling methods for collecting data?
TRANSCRIPT
• How do I study different sampling methods for collecting data?
When a random sample of size n is taken from a large population, the margin of error is approximated by:
7.5 Select and Draw Conclusions from Samples
Margin of Error Formula
Margin of error = n
1
Which means that if the percent of the sample
responding a certain way is p (expressed as a
decimal), then the percent of the population that
would respond the same way is likely to be between
p – ____
and p + ____
. n
1
n
1
Self-selected sampling:
7.5 Select and Draw Conclusions from Samples
Types of Sampling
The person conducting the survey chooses the people he/she wants to participate in the survey.Systematic sampling:Involves a random start and then proceeds with the selection of every kth element from then onwards.Convenience sampling:A sample population is selected because it is readily available and convenient.
Random sampling:A sampling where each member of the population has an equal and known chance of being selected.
7.5 Select and Draw Conclusions from Samples
Example 1 Classify samplesClassify samples
A student wants to survey everyone at A student wants to survey everyone at his school about the quality of the his school about the quality of the school’s assemblies. Identify the type of school’s assemblies. Identify the type of sample described as a sample described as a self-selected self-selected samplesample, a , a systematic samplesystematic sample, a , a convenience sampleconvenience sample, or a , or a random samplerandom sample..a.a. The student surveys every 8The student surveys every 8thth student student
that enters the assembly.that enters the assembly.Solutiona. The student uses a rule to select students, so the
sample is a ____________ sample.systematic
7.5 Select and Draw Conclusions from Samples
Example 1 Classify samplesClassify samples
A student wants to survey everyone at A student wants to survey everyone at his school about the quality of the his school about the quality of the school’s assemblies. Identify the type of school’s assemblies. Identify the type of sample described as a sample described as a self-selected self-selected samplesample, a , a systematic samplesystematic sample, a , a convenience sampleconvenience sample, or a , or a random samplerandom sample..b.b. From a random lottery, the student chooses From a random lottery, the student chooses
125 students and teachers to survey.125 students and teachers to survey.Solutionb. The student chooses from a random name lottery,
so the sample is a __________ sample.random
7.5 Select and Draw Conclusions from Samples
1. A local mayor wants to survey
local area registered voters. She
mails surveys to the individuals
that are members of her political
party and uses only the surveys
that are returned.
Checkpoint. Identify the type of sample described.Checkpoint. Identify the type of sample described.
She selected the ones that she wanted to survey.
sample selected-self
7.5 Select and Draw Conclusions from Samples
Example 2 Identify biased solutionsIdentify biased solutions
Tell whether each sample in Example 1 Tell whether each sample in Example 1 is is biasedbiased or or unbiasedunbiased. Explain your . Explain your reasoning.reasoning.
a.a. The student surveys every 8The student surveys every 8thth student that enters the assembly.student that enters the assembly.
Solution
a. The sample is ____________ because the student surveys the students, but not the teachers.
biased
7.5 Select and Draw Conclusions from Samples
Example 2 Identify biased solutionsIdentify biased solutions
Tell whether each sample in Example 1 Tell whether each sample in Example 1 is is biasedbiased or or unbiasedunbiased. Explain your . Explain your reasoning.reasoning.
b.b. From a random lottery, the student From a random lottery, the student chooses 125 students and teachers to chooses 125 students and teachers to surveysurvey..
Solution
b. The sample is ____________ because both students and teachers are surveyed.
unbiased
7.5 Select and Draw Conclusions from Samples
2. Tell whether the sample in
Exercise 1 is biased or unbiased.
Explain your reasoning.
Checkpoint. Complete the following exercises.Checkpoint. Complete the following exercises.
Because the survey is mailed to only those who are members of one political party.
biased
7.5 Select and Draw Conclusions from Samples
Example 3 Find a margin of errorFind a margin of error
Newspaper Survey In a survey of 325 Newspaper Survey In a survey of 325 students and teachers, 30% said they read students and teachers, 30% said they read the school’s newspaper every weekday.the school’s newspaper every weekday.a.a. What is the margin of error for the What is the margin of error for the
survey?survey?Solutiona. Margin of error =
n
1
1
325_____ 055.0
The margin of error for the survey is about ______%.5.5
7.5 Select and Draw Conclusions from Samples
Example 3 Find a margin of errorFind a margin of error
Newspaper Survey In a survey of 325 Newspaper Survey In a survey of 325 students and teachers, 30% said they read students and teachers, 30% said they read the school’s newspaper every weekday.the school’s newspaper every weekday.b.b. Give an interval that is likely to contain the Give an interval that is likely to contain the
exact percent of all students and teachers who exact percent of all students and teachers who read the school newspaper every weekday.read the school newspaper every weekday.
Solutionb. To find the interval, add or subtract _____%.5.5
%____%____%30 5.5 5.24%____%____%30 5.5 5.35
It is likely that the exact percent of all students and teachers who read the school’s newspaper every weekday is between _____% and _____%.5.24 5.35
7.5 Select and Draw Conclusions from Samples
3. In Example 3, suppose the
sample size is 400 students and
teachers. What is the margin of
error for the survey?
Checkpoint. Complete the following exercises.Checkpoint. Complete the following exercises.
n
1
400
1 05.0 %5
7.5 Select and Draw Conclusions from Samples
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