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 his study, Joe should ensure that the sample is representative of the entire population of U.S. adults. One approach to achieve this is through stratified random sampling.
Step 1: Determine the sample size for each state
Since Joe wants to have 10,000 adults in total, with equal representation of males and females, he would have 5,000 males and 5,000 females in his sample.
Step 2: Calculate the proportion of U.S. adults in each state
Joe needs to find the proportion of U.S. adults residing in each of the 50 states. This information can be obtained from the Census Bureau or other credible sources.
Step 3: Calculate the sample size for each state
Multiply the proportion of U.S. adults in each state by the desired sample size (10,000 adults) to determine the number of individuals to include from each state. This will ensure that the states with larger populations contribute a proportionally larger number of participants.
Step 4: Round the sample size
Round the sample size for each state to the nearest whole number to ensure practicality.
Step 5: Randomly select individuals
From each state, Joe must randomly select the determined number of individuals to include in his study. This can be done using different methods, such as random number generators or lottery systems.
By following these steps, Joe will obtain a stratified random sample that represents the U.S. adult population from all 50 states, ensuring a minimized bias in his study.
To avoid bias in the study, Joe should choose a random sample of individuals from each state proportional to the state's population size.
According to the U.S. Census Bureau, the total U.S. population in 2020 was approximately 331 million. Dividing this number by 50 states gives an average population size of roughly 6.6 million people per state.
Assuming each state's population is evenly distributed between males and females, Joe should randomly choose 100 individuals from each state (50 males and 50 females) to reach his desired sample size of 10,000 adults.
Therefore, to avoid bias in his study, Joe should choose 100 individuals (50 males and 50 females) from each of the 50 states.