Final answer:
The question relates to recalculation of the sample mean and sample proportion upon adding new data. Both the sample mean and sample proportion could change, depending on the new data points. Proportion problems are associated with categorical data and use normal distribution techniques.
Step-by-step explanation:
The question concerns the calculation of the sample mean and sample proportion when new data is added to a sample. From provided options, without additional information or context, it is not possible to determine the specific changes to the mean and proportion. However, generally speaking, the sample mean may change when new data points are added, as it is the average of all the sample data points. The sample proportion, which is the ratio of the number of successes to the total number of trials, could also change if additional successes or failures are included in the sample.
Recalculation of these statistics depends on the new data. If the mean or the proportion were to remain the same, the total of the new data points added would need to maintain the current ratio or average. In most cases, unless the new data points are identical to the current mean or closely maintain the success/failure ratio, both the new sample mean and sample proportion would change when recalculated with additional data.
You may encounter proportion problems when dealing with categorical data where outcomes are divided into two categories, such as 'Success or Failure' or 'Yes or No'. For example, estimating the population proportion of voters for a particular candidate or the proportion of the population with a college-level education. Proportion calculations follow a normal distribution, as described by the central limit theorem, when the sample size is sufficiently large.