Final answer:
It is false that there's a 100% chance a sample proportion is always in the confidence interval. A confidence interval at a certain level suggests only a corresponding percentage of such intervals will contain the true population parameter in repeated sampling.
Step-by-step explanation:
The statement is false; there is not a 100% chance that our observed sample proportion of U.S. adults who can correctly interpret a scatterplot is contained in the confidence interval. When we discuss confidence intervals in statistics, we're talking about the range of values, centered around a sample statistic, that is likely to contain the true population parameter with a certain confidence level. It means that, given the level of confidence and the methodology used, we expect a certain proportion of the confidence intervals from repeated samples to contain the true population parameter.
For example, if you have a 95% confidence level, it means that if you were to take 100 different samples and calculate a confidence interval for each sample, you would expect about 95 of those confidence intervals to contain the true parameter. But this does not guarantee that any single given confidence interval definitely contains the true parameter. Likewise, if a confidence level is 90%, then we'd expect 90 out of 100 confidence intervals to actually include the true mean or proportion.
In general, changing the confidence level alters the width of the confidence interval. A higher confidence level, such as 99% compared to 90%, results in a wider confidence interval, reflecting greater uncertainty, while still capturing the true parameter in more instances across different samples.