Joe wants to find out the most common source of a news among US adults. He wants to sample to have 10,000 adults half male and half female individuals to make a valid generalization how many people from each of 50 states should we choose randomly to avoid bias in his study.
To avoid bias in Joe's study, he should aim to select a representative sample from each of the 50 states. One way to do this is to use a proportional stratified sampling technique, where the number of individuals selected from each state is proportionate to the state's population size.
First, Joe would need to find out the population distribution of each state in the US. He can use the latest census data or other reputable sources to determine the population of each state.
Let's assume that Joe has accurate population data for each state. He can then calculate the percentage of the total US population that each state represents. Joe can then use these percentages to determine how many individuals he should sample from each state.
For example, if State A represents 5% of the total US population, Joe should aim to select 5% of his sample (500 individuals) from State A. He should repeat this process for all 50 states.
By using this proportional stratified sampling approach, Joe can ensure that his study is not biased towards any particular state and that his results accurately represent the opinions of US adults as a whole.