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, he should aim to select a random sample of 10,000 adults from all 50 states in the U.S. Since Joe wants equal representation of male and female individuals, he would need to select half of the sample as males and the other half as females.
First, we can calculate the number of individuals needed from each gender. Since Joe wants a total sample size of 10,000, he would need 5,000 individuals of each gender.
Next, we divide the total sample size equally across the 50 states. Since we want to avoid bias, we should aim to include individuals from each state proportionally. Assuming an equal distribution of population across states, we can allocate an equal number of individuals from each state.
To determine the number of individuals needed from each state, we divide the total sample size by the number of states. In this case, 10,000 divided by 50 gives us 200 individuals per state.
Thus, Joe should randomly select 200 individuals from each of the 50 states to avoid bias in his study.
There are 50 states in the United States of America.
How many states are there in usa?
To avoid bias, Joe should choose a random sample of adults from all 50 states in proportion to their population. According to the 2020 Census, the population of each state varies widely. Here are the populations of the 10 most populated states:
1. California - 39,538,223
2. Texas - 29, 78,991
3. Florida - 21, 538, 187
4. New York - 20, 201, 249
5. Pennsylvania - 13,002,700
6. Illinois - 12,812,508
7. Ohio - 11,799,448
8. Georgia - 10,711,908
9. North Carolina - 10,439,388
10. Michigan - 10,077,331
To determine the number of individuals Joe should choose from each state, he can use the following formula:
(Number of individuals from state) = (Population of state / Total U.S. population) * Sample size
Using this formula, here's how many individuals Joe should select from the 10 most populated states:
1. California - (39538223/331449281) * 5000 = 59 individuals
2. Texas - (29789991/331449281) * 5000 = 45 individuals
3. Florida - (21538187/331449281) * 5000 = 32 individuals
4. New York - (20201249/331449281) * 5000 = 30 individuals
5. Pennsylvania - (13002700/331449281) * 5000 = 19 individuals
6. Illinois - (12812508/331449281) * 5000 = 19 individuals
7. Ohio - (11799448/331449281) * 5000 = 18 individuals
8. Georgia - (10711908/331449281) * 5000 = 16 individuals
9. North Carolina - (10439388/331449281) * 5000 = 16 individuals
10. Michigan - (10077331/331449281) * 5000 = 15 individuals
Joe should repeat this calculation for all 50 states to obtain the total number of individuals he should select from each state.