Final answer:
The questions are related to statistical analysis and include concepts such as sample size adequacy, representativeness of results for a population, hypothesis testing with distributions like binomial or normal, and determining the necessary sample size for a desired level of confidence in survey results.
Step-by-step explanation:
The questions presented are all centered around the theme of statistical analysis and probability, within the subset of mathematics known as statistics. They involve conducting surveys, interpreting results, assessing sample sizes, and performing hypothesis testing. For example, when considering whether the sample size of 3,274 people is large enough, it’s necessary to look at the total population size and desired level of confidence and margin of error. Typically, a sample size of over 1,000 is considered robust for general population surveys, but this can vary based on specific conditions and research goals.
In the case of whether sample percentages accurately reflect the U.S. population for individuals born since 1971, the assessment should be based on the sampling method and representativeness of the sample. It becomes a matter of whether the sample fits the demographic and whether there are biases in data collection. For performing a hypothesis test regarding preference for a brand, a typical distribution to use would be the binomial distribution or normal approximation to the binomial, depending on the sample size and the conditions of the Central Limit Theorem.
Decisions on the required sample size for a certain level of confidence, like the internet marketing company wanting to be 90% confident within a 5 percentage point margin of error, involve calculations using z-scores and the standard error of the proportion. These are all common practices in statistical analysis for understanding and making inferences about a population based on sample data.