Answer :
Answer:
We are 95 percent confident that the mean word length for all papers submitted by students in humanities programs is between 20,995 words and 22,905 words
Step-by-step explanation:
The confidence interval is used to predict the mean for the entire humanities program, not just the sample.
Final answer:
The 95 percent confidence interval for the word count of papers means we are 95 percent confident that the true average word count lies within the interval, not that 95 percent of the papers fall within this range.
Explanation:
A 95 percent confidence interval, like the one given as (20,995, 22,905) for the word length of papers, does not mean that 95 percent of the student papers contain between 20,995 and 22,905 words. Instead, it means that we are 95 percent confident that the true average word count of all papers is contained within this interval. If we were to take many samples and build a confidence interval from each one, we would expect 95 percent of those intervals to contain the true population mean.
When we report a confidence interval, it is a way of showing the range within which the true population parameter (in this case, the mean word count of student papers) is expected to lie, given a certain level of confidence. It is not a reflection of the individual sample data, but rather an estimate based on that sample that allows us to predict about the population from which it was drawn.
The width of the confidence interval can vary depending on the level of confidence we seek. A 90 percent confidence interval will be narrower, reflecting less certainty that the interval contains the true population mean, whereas a 95 percent confidence interval is wider, accommodating more certainty.
