Joe wants to find the most common source of news among U.S. adults. He wants his sample to have 10,000 adults (half male and half female individuals) to make a valid generalization. How many people from each of the 50 states should he choose randomly to avoid bias in his study
To avoid bias in Joe's study and ensure a valid generalization, he should choose a random sample that is proportional to the population distribution of the 50 states. Here's how Joe can calculate the number of people he should choose from each state:
1. Determine the total population of U.S. adults: According to the U.S. Census Bureau, the estimated population of U.S. adults in 2021 is approximately 258 million.
2. Calculate the population proportion of each state: Divide the population of each state by the total U.S. adult population. This will give you the proportion of adults in each state relative to the entire U.S. adult population.
3. Multiply the population proportion of each state by the desired sample size: Since Joe wants a sample of 10,000 adults, he can multiply the population proportion of each state by 10,000 to find out how many adults he should choose from that state.
4. Round the resulting number to the nearest whole number: Round the number of adults to be chosen from each state to the nearest whole number to obtain a practical sample size.
By following these steps, Joe can obtain a random sample that is representative of the U.S. adult population in each state, ensuring the avoidance of bias in his study.