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?(1 point)
Joe should choose 200 adults from each of the 50 states, ensuring that he has a representative sample from across the entire country.
You want to estimate the number of students who bring their lunch to school every day. Which of the following is the best sample for this situation?(1 point)
Responses
80 students selected at random during lunch
80 students selected at random during lunch
all members of the Math Club
all members of the Math Club
45 first-year students selected at random
45 first-year students selected at random
50 female students selected at random
The best sample for this situation would be 80 students selected at random during lunch as it would give a representative sample of all students who bring their lunch to school.
A coffee shop owner is interested in determining what people think about the new coffee flavor. Which of the following is the population in this situation?(1 point)
Responses
the first 50 customers who bought the new coffee
the first 50 customers who bought the new coffee
all customers who did not buy the new coffee
all customers who did not buy the new coffee
all customers who bought the new coffee
all customers who bought the new coffee
100 random customers
100 random customers
The population in this situation is all customers who bought the new coffee, as the coffee shop owner wants to determine what people think about the new coffee flavor, which is limited to only those who bought the new coffee.
Tom wants to know the average number of musical instruments students in his school play. He used the school’s two band classes, consisting of a total of 48 students, as his representative sample. He concluded that students in his school play an average of three musical instruments. Is his conclusion valid?(1 point)
Responses
Yes, because all members of the sample play at least one musical instrument.
Yes, because all members of the sample play at least one musical instrument.
No, because he did not choose students randomly.
No, because he did not choose students randomly.
Yes, because the sample includes both males and females who play musical instruments.
Yes, because the sample includes both males and females who play musical instruments.
No, because his representative sample is too large.
No, because he did not choose students randomly. The representativeness of a sample depends not only on its size, but also on the way it is selected. Because Tom did not choose students randomly, his conclusion may be biased and not representative of the entire school population.
The population in this situation refers to the group of individuals who are being studied or observed. In this case, the coffee shop owner is interested in determining what people think about the new coffee flavor. Therefore, the population would be all customers who bought the new coffee (option C).
Yes, that is correct. The population in this situation is all customers who bought the new coffee, as the coffee shop owner wants to determine what people think about the new coffee flavor, which is limited to only those who bought the new coffee.
To avoid bias in Joe's study, he should select a random sample from each of the 50 states in proportion to their population. This ensures representation from each state, as the news habits of U.S. adults can vary across regions. Here's how Joe can determine the number of people he should choose from each state:
1. Determine the total population of the United States: According to the latest data, the population of the United States is approximately 331 million.
2. Calculate the proportion of the population for each state: Divide the population of each state by the total U.S. population. This will give Joe the relative weight of each state's population in his study.
3. Multiply the proportion of each state's population by the desired sample size: To determine the number of people Joe should choose from each state, multiply the proportion of the state's population by 10,000 (half for male and half for female individuals).
4. Round the calculated numbers: Since Joe cannot select a fraction of a person, he should round the numbers he calculated in step 3 to the nearest whole number.
By following this approach, Joe will be able to ensure that his sample is representative of the U.S. adult population across all states and minimize bias in his study.