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Hey there! Today we're going to learn how to use a random sample to make smart predictions about a whole group's banking habits.
A population is an entire group you want to learn about, like all 800 eighth-graders at your school. Studying everyone takes too long, so we use a random sample, which is a small, randomly picked group that represents the whole population.
To make an inference about the full population, we set up a proportion using data from our random sample. If 12 out of 30 surveyed students have a savings account, we can predict that same ratio applies to all 800 students.
We analyze the sample fraction by setting it equal to x over the total population size. Solving the proportion gives us a clear inference about how many total people share that habit.
A bank surveys a random sample of 50 workers in a town of 2,000 workers. In the sample, 35 workers direct-deposit their paychecks into a checking account. Infer how many total workers in the town use direct deposit.
- Identify the sample ratio of workers using direct deposit: 35 out of 50.
- Write the sample ratio as a fraction: 35 / 50, which simplifies to 7 / 10.
- Set up a proportion to represent the entire population of 2,000 workers: 7 / 10 = x / 2,000.
- Multiply the denominator (2,000) by the fraction (7 / 10) to solve for x: 2,000 * 7 = 14,000, and 14,000 / 10 = 1,400.
- Conclude that based on the random sample, about 1,400 workers in the town use direct deposit.
