there are 3,000 people at a concert you survey a random sample of 200 people and find that for 35 of them this is the first concert they have ever attended estimate how many total people are attending their first concert that night
There are different ways to approach this problem, but one common method is to use the concept of proportions. Specifically, since we have a sample proportion (35/200) of people who are attending their first concert, we can use it to estimate the population proportion (P) and then multiply it by the population size (N) to get the estimated number of people in the population who fit that category.
To do this, we first assume that the sample proportion is a reasonably accurate reflection of the population proportion, which means we can use it as our point estimate. In other words, we assume that P = 35/200 = 0.175. This means that if we randomly selected a person from the entire population of concert-goers, the probability that they are attending their first concert is 0.175.
Next, we use this proportion to estimate the total number of such people in the whole population. This is done by multiplying it by the total population size (N), which gives:
Estimated number of first-time concert-goers = P*N
= 0.175 * 3000
= 525
Therefore, based on our sample of 200 people, we estimate that there are about 525 people in total who are attending their first concert that night. Note that this is just an estimate and comes with some level of uncertainty due to sampling variability and potential biases. Also, the assumptions and methods used here should be justified and verified before applying them to other situations.
can you make it way shorter and way simpler
Number of first-time concert-goers = (35/200) x 3000 = 525.
To estimate the total number of people attending their first concert that night, you can use the concept of sampling and extrapolation.
Step 1: Calculate the percentage of people in the sample who attended their first concert.
- Divide the number of people in the sample who attended their first concert (35) by the total sample size (200).
- 35/200 = 0.175 (or 17.5% expressed as a decimal).
Step 2: Use the calculated percentage to estimate the total number of people attending their first concert.
- Multiply the percentage from Step 1 by the total number of people at the concert.
- 0.175 * 3,000 = 525.
Based on the surveyed sample, you can estimate that approximately 525 people are attending their first concert that night.