at the census bureau web site you can find the percent of adults in each state who have at least a bachelors degree. it makes no sense to find the mean for these data and use it to get a confidence interval for the mean percent U in all 50 states. Why not?

The fraction of people with a college degree in all states would require a WEIGHTED mean of the individual state averages, with the weighting done by population. The populations of states vary by a large factor. California has 50 times more people than North Dakota, for example.

It does make sense to find the mean for these data and use it to get a confidence interval for the mean percent in all 50 states. However, there are a few reasons why it may not be ideal to do so:

1. Sample Bias: The data available on the census bureau website represents the percent of adults in each state who have at least a bachelor's degree. This data may not be a random sample that represents the entire population of adults in all 50 states. There may be certain demographic or geographic biases in the sample, which would affect the generalizability of the mean.

2. Lack of Variation: In some states, the percentage of adults with at least a bachelor's degree may be very high, while in others it may be very low. If there is a lack of variation in the data, calculating a confidence interval for the mean may not provide meaningful information about the population as a whole.

3. Confidence Interval Interpretation: When calculating a confidence interval for the mean, it is important to consider the margin of error. In cases where the sample size is relatively small, the margin of error can be quite large, making the confidence interval less precise and less useful for making accurate predictions about the population.

In summary, while it is possible to calculate a mean and confidence interval for the percent of adults with at least a bachelor's degree in each state, it is important to consider potential biases, variations in the data, and the interpretability of the confidence interval.

To understand why it is not appropriate to find the mean and use it to calculate a confidence interval for the mean percentage of adults with at least a bachelor's degree in all 50 states, we need to consider the nature of the data and the limitations of using a mean and confidence interval in this context.

The data from the Census Bureau website provides the percent of adults in each state who have at least a bachelor's degree. These percentages are individual observations for each state and represent separate populations. Each state has its own unique population composition and educational attainment rates, making the data inherently non-comparable.

Given that the data represents independent percentages for separate populations, it does not make sense to calculate a mean by aggregating the percentages across all states. The concept of a mean assumes that the values being averaged are statistically meaningful and can be added or combined together.

In the case of percentage data, summing them up and taking the average does not hold meaning. For example, averaging 50% and 10% would yield 30%, which is statistically nonsensical. Calculating a mean for non-comparable percentages can distort the true representation of the data and mislead the interpretation and subsequent analysis.

Additionally, confidence intervals are typically calculated around the mean to estimate the true population mean of a single variable. However, in this case, we are dealing with multiple populations, each with its own degree of educational attainment.

Instead of calculating a mean and confidence interval for the overall percent of adults with at least a bachelor's degree across all 50 states, it would be more appropriate to calculate separate confidence intervals for each state individually. This approach accurately captures the variability and distribution of educational attainment within each state's population.

In summary, due to the independent nature of the data representing different populations, it is not appropriate to calculate a mean and use it to find a confidence interval for the mean percentage of adults with at least a bachelor's degree across all 50 states. Instead, confidence intervals should be calculated separately for each state to accurately represent the variability within each population.