A survey was given to a random sample of 400 people living in a certain community. The people were asked whether they supported the construction of walking trails in the community park. The results are shown in the following table.

Response Frequency
Yes, support 210
No, do not support 90
No opinion 100
Total 400

A follow-up study will be conducted with a sample of 20 people from the 300 people who responded yes (support) and no (do not support). Two sampling methods have been proposed: a simple random sample and a stratified random sample with the survey response as strata.

(b) If the stratified random sample is used, what is the number of people that will be selected from those who responded yes? Support your answer by showing your work.

Using simple random sampling for the follow up data will involve making a random selection of 20 participants from the 300 people such that each of the 300 participants have an equal chance of being selected. A random number generator could be employed in making a simple random sample in this scenario.

For Stratified random sampling, participants are first divided into stratas, in this case, the stratas are (Yes and No responses). Then a random sample of participants is are chosen from each strata based on the number of participants in each strata.

B)

If a stratified random sampling is employed, the number of 'Yes' respondents which will be chosen can be calculated thus :

(210 / 300) × 20

0.7 × 20 = 14 people.

Therefore, 14 people would be selected from those who responded 'yes' to be a part of the sample.

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The total number of people that will be selected is 14.

Explanation:

In the case of stratified random sampling, we first need to split the population into several strata and then select a sample from each. For a given question, the solution type is

Sample size of strata = (Scale of whole sample by population size) multiply strata size

= (20 by 300) multiply 210

After we have resolved, 14 or 14 persons will be chosen.

One value is that here, as we split all the data into strata and then pick samples from them so that they can be used as a protection against unnecessary samples and to have more precise sample measurements. Here, because we needed samples from the population that provided yes and no opinion so that it is easier to use stratified sampling method then if we use simple random sampling then we can use those samples that did not offer an opinion. But since we're not using this form, we can stop it.

answer; fire resistant covered containers, until removed

light-year  

the distance that light travels in a vacuum in one year, equal to about 9.46 trillion km (5.88 trillion mi). light-years are used in measuring interstellar and intergalactic distances.  

parsec  

a unit of distance used in astronomy, equal to about 3.25 light years (3.08 × 1016 meters).  

parallax  

the apparent angular displacement of a celestial body due to its being observed from the surface instead of from the center of the earth (diurnal parallax or geocentric parallax) or due to its being observed from the earth instead of from the sun (annual parallax or heliocentric parallax)  

absolute magnitude  

the magnitude (brightness) of a celestial object as it would be seen at a standard distance of 10 parsecs.  

apparent magnitude  

the magnitude of a celestial object as it is actually measured from the earth.  

redshift  

an increase in the wavelength of radiation emitted by a celestial body as a consequence of the doppler effect.  

the great thing about your imagination is that it doesn't have to make sense! if i were you i would be stuck in space, no communication with earth travelling around and around, you can only guess how long its been since your communication broke down. you land on an undiscovered planet, you do a scientific investigation examining the elements and conditions. you come across alien lifeforms.  

best of luck!