Question

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.

Answer 1

If the stratified random sample is used, the number of people that will be selected from those who responded "yes" can be determined by considering the proportion of "yes" responses in the overall sample.

In the given table, the total number of respondents who support the construction of walking trails in the community park is 210. This represents a proportion of 210/400, or 0.525.

To calculate the number of people that will be selected from those who responded "yes" in the follow-up study, we need to apply this proportion to the new sample size of 20.

So, the number of people that will be selected from those who responded "yes" can be calculated as follows:

Number of people selected from those who responded "yes" = Proportion of "yes" responses * Sample size

= 0.525 * 20

= 10.5

Since you cannot select a fraction of a person, you need to round the number to the nearest whole number. In this case, the number of people selected from those who responded "yes" in the stratified random sample would be 11.

Step-by-step explanation: