# Random Sampling

Lab 3C

### Learning by sampling

• In many circumstances, there's simply no feasible way to gather data about everyone in a population.

• For example, the Department of Water & Power (DWP) wants to determine how much water people in Los Angeles use to take a shower. They've created a survey to pass out to collect this information.
• Write down two reasons why getting everyone in Los Angeles to fill out the survey would be difficult. Also, write a sentence why the DWP might consider using a sample of households instead.
• In this lab, we'll learn how sampling methods affect how representative a sample is of a population.

• In previous labs, we used the cdc data as a sample for young people in the United States.
• In this lab, we'll consider these survey respondents to be our population.
• Load the cdc data into R and fill in the blanks to take a convenience sample of the first 50 people in the data:
s1 <- slice(____, 1:____)

• Why do you think we call this method a convenience sample?

• A convenience sample is a sample from a population where we collect data on subjects because they're easy-to-find.
• Using your convenience sample, create a bargraph for the number of people in each grade.
• Do you think the distribution of grade for your sample would look similar when compared to the whole cdc data?
• Which groups of people do you think are over or under represented in your convenience sample? Why?
• Create a bargraph for grade using the cdc data.
• Compare the distributions of the cdc data and your convenience sample and write down how they differ.

### Using randomness

• Fill in the blanks below to create a sample by randomly selecting 50 people in the cdc data, without replacement. Call this new sample s2:
___ <- sample(___, size = ___, replace = ___)

• Write a sentence that explains why you think the distribution of grade for this random sample will look more or less similar to the distribution from the whole cdc data.
• Create a bargraph for grade based on this random sample to check your prediction.

### Increasing sample size

• Create bargraphs for grade based on each of the following sample sizes: 10, 100, 1,000, 10,000.
• Compare each distribution to that of the population.
• How do the distributions change as the size of the sample increases? Why do you think this occurs?
• tally() the proportion of grades for your convenience sample and all your random samples.
• Which set of proportions looks most similar to the proportions of the population?

### Lessons learned

• The mean, or proportion, from a random sample might not always be closer to that of the true population when compared to a convenience sample.
• However, as sample sizes get larger:
• Random samples will tend to be better estimates for the population.
• With convenience samples, this might not be the case.
• Write down a reason why estimates based on convenience samples might not improve even as sample size increases.