A sample of 30 of 178 funded projects revealed that 12 were valued at $17,360 each and 18 were valued at $20,280 each. From the sample data, estimate the total value of the funding for all the projects. (Enter your answers to two decimal places.)
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To estimate the total value of the funding for all the projects, we can use the concept of sampling.
Given that we have a sample of 30 projects out of 178 funded projects, and we know the values of 12 projects ($17,360 each) and 18 projects ($20,280 each), we can calculate the average value per project in the sample.
To do this, we add up the values of all the projects in the sample and divide it by the number of projects in the sample. So, for 12 projects valued at $17,360 each and 18 projects valued at $20,280 each, the total value of the projects in the sample is:
(12 * $17,360) + (18 * $20,280) = $208,320 + $365,040 = $573,360
The average value per project in the sample can be calculated by dividing the total value of the projects in the sample by the number of projects in the sample:
$573,360 / 30 = $19,112
Now, to estimate the total value of the funding for all the projects, we can use the concept of proportion and apply it to the entire population of 178 projects.
We set up the proportion:
(30 projects in the sample) : (178 projects in the population) = ($573,360 total value in the sample) : (x total value in the population)
Cross-multiplying:
30 * x = 178 * $19,112
Simplifying:
30x = $3,398,336
Dividing both sides by 30:
x = $3,398,336 / 30
Therefore, the estimated total value of the funding for all the projects is:
x ≈ $113,278.13
So, the estimated total value of the funding for all the projects is approximately $113,278.13.