2.2 Sabrina notes random sampling and MOE

Objectives

Estimate population means and proportions and develop margin of error from simulations involving random sampling. Analyze surveys, experiments, and observational studies to judge the validity of the conclusion.

Vocabulary simple random sample systematic sample stratified sample cluster sample convenience sample self-selected sample probability sample margin of error

Which are random Sampling methods?

Which are nonrandom Sampling methods?

When a survey is used to gather data, it is important to consider how the sample is selected for the survey. If the sampling method is biased, the survey will not accurately reflect the population.

Most national polls that are reported in the news are conducted using careful sampling methods in order to minimize bias.

Other polls, such as those where people phone in to express their opinion, are not usually reliable as a reflection of the general population Remember that a random sample is one that involves chance. Six different types of samples are shown below.

The campaign staff for a state politician wants to know how voters in the state feel about a number of issues. Classify each sample.

A. They call every 50th person on a list of registered voters in the state.

B. They randomly select 100 voters from each county to call.

Use the Venn Diagram to compare and contrast systematic vs. stratified sampling

Systematic Stratified

C. They ask every person who comes to the next campaign rally to fill out a survey. D. The local news asks its viewers to call-in or text their opinions.

Self-selected Use the Venn Diagram to compare and contrast self-selected vs. convenience sampling

Convenience

E. They randomly select 100 voters from each county to call. F. They randomly select 5 counties from the region and contact every voter within each of those counties.

Stratified Use the Venn Diagram to compare and contrast stratified vs. cluster sampling

Cluster

A community organization has 56 teenage members, 103 adult members, and 31 senior members. The council wants to survey the members. Classify each sampling method. Which is most accurate? Which is least accurate? Explain your reasoning.

Method A: simple random Method B: systematic Method C: Stratified

Method A is the most accurate because every member of the population is equally likely to be in the sample. In Method C, the sample contains an equal number from each group, but the total numbers in each group differ significantly. So, adults are underrepresented and seniors are overrepresented. Method B is the least accurate because members who do not attend the cleanup have no chance of being included.

A small-town newspaper wants to report on public opinion about the new City Hall building. Classify each sampling method. Which is most accurate? Which is least accurate? Explain your reasoning.

Method A: self-selected sample Method B: convenience sample Method C: cluster sample Method A is the least accurate because only people who are willing to volunteer their opinions are chosen. Method B is also inaccurate because only students and only those in the cafeteria are surveyed. Method C is the most accurate because different groups are randomly chosen and then all members of the chosen group are surveyed.

Application: Two classes each had 10 qualified students volunteer for junior cabinet. Only 4 students total can be selected. Ms. Mashburn decides that she must randomly select the 4 to serve. Class A: Class B: Allison Jason Annie John Belinda Keith Barbara Ken Calissa Lon Corinne Lewis Jennifer Mark Judy Mike Margaret Ned Madison Norm Explain how could you help Ms. Mashburn choose the 4 students randomly. Implement each sampling strategy by using the table of random digits below. Write down who was chosen.

SRS...Simple Random Sample Step 1: Give each student a unique two digit number. Since there are 20 students, you can number them from 00-19.

start here....

Step 2: Decide where to start in the table of random digits. Look at two digits at a time. If it you find a number between 00 and19, find the associated student and select him/her for your sample. Continue this process until you find 4 unique students.

Sample chosen: _______________, ______________ ___________________, ____________________

Systematic Sample

Step 1: Give each student a unique two digit number. Step 2: Use the table of random digits to randomly pick the first student in your sample. Then choose start every 20/4 = 5th student from the one randomly chosen.

here....

Sample: _________, ___________ ____________, _____________

Step 1: Give each student a two digit number.

Stratified Random Sample...by gender

Step 2: Use your table of digits to pick until you get two unique girls and 2 unique boys. Ignore repeated values. Also, if you select two girls first, then ignore all other girls and continue until you get two boys.

start here....

Sample: ____________, ______________ ______________, ________________

Step 1: Give each cluster a number. Since there are 5 groups, you can assign them the numbers from 00-04.

Cluster Sample

Step 2: Use the table until you find a number between 00-04. Everyone in that group will be in your sample.

start here....

Sample: ____________, ______________ ______________, ________________

The margin of error of a random sample defines an interval, centered on the sample percent, in which the population percent is most likely to lie

A city is about to hold an election. According to a survey of a random sample of city voters, 42% of the voters plan to vote for Poe and 58% of the voters plan to vote for Nagel. The survey’s margin of error is ±7%. Does the survey clearly project the outcome of the voting? Between 35% and 49% of all voters plan to vote for Poe and between 51% and 65% of all voters plan to vote for Nagel. Because the intervals do not overlap, the survey does clearly project the outcome of the voting.

A survey of a random sample of voters shows that 38% of voters plan to vote for Gonzalez, 31% of voters plan to vote for Chang, and 31% plan to vote for Harris. The survey has a margin of error of ±3%. Does the survey clearly project the outcome of the voting? Explain. Yes; while there is overlap between the intervals for Chang and Harris, their intervals, which are from 28% to 34%, do not overlap the interval for Gonzalez, which is 35% to 41%.