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.)
$ 35.60 was my answer
this is how I worked it 12+18=30, 12/30=.4, .4X178=71.2
12+18=30, 18/30=.6, .6X178=106.8
I first got 178.00 then I redone and got 35.60
Can someone tell me what I am doing wrong on this problem?
To estimate the total value of the funding for all the projects, we can use the concept of sampling and the method of ratio estimation.
First, let's calculate the ratio of the sampled projects to the total projects:
Ratio of sampled projects = (Sample size / Total size) = (30 / 178)
Next, let's calculate the ratio of the values of the sampled projects to the total value:
Ratio of sampled values = (Sampled value for $17,360 projects * Number of $17,360 projects + Sampled value for $20,280 projects * Number of $20,280 projects) / Total value
= ((12 * 17360) + (18 * 20280)) / Total value
Now, we can calculate the estimated total value of the funding for all the projects:
Estimated total value = Ratio of sampled values / Ratio of sampled projects
= ((12 * 17360) + (18 * 20280)) / (30 / 178)
By simplifying this equation, you will get the estimated total value of the funding for all the projects, which should not be $35.60 but a larger value. Let me calculate that for you.
Calculating the estimated total value:
Estimated total value = ((12 * 17360) + (18 * 20280)) / (30 / 178)
Estimated total value = (208320 + 365040) / (0.16853932)
Estimated total value = 573360 / 0.16853932
Estimated total value ≈ 3,404,331.30
Therefore, the estimated total value of the funding for all the projects is approximately $3,404,331.30.