Question

a graduate student wanted to estimate the average time spent studying among graduate students at her school. she randomly sampled graduate students from her school and obtained a 99% confidence interval of (17.3,22.5) hours/week. in the context of the problem, which of the following interpretations is correct?
choose the correct answer below.
a. graduate students at this students school study between 17.3 and 22.5 hours per week 99% of all weeks during the year
b. approximately 99% of all random samples of graduate students from this school will give a mean number of hours studied per week between 17.3 and 22.5
c. we are 99% sure that the average amount of time spent studying among graduate students at this students school is between 17.3 and 22.5 hours per week
d. there is a 99% chance that the average amount of time spent studying for all graduate students at this students school is between 17.3 and 22.5 hours per week
e. at this students school 99% of all graduate students study between 17.3 and 22.5 hours per week on average

Explanation:

A confidence interval gives a range of values within which we are a certain percentage (in this case, 99%) confident that the population parameter (here, the average amount of time spent studying by all graduate students at the school) lies. Option C correctly interprets the 99% confidence interval. Option A misattributes the 99% to all weeks, option B misinterprets the 99% for samples, option D misrepresents the chance as a probability for the interval containing the mean (it's a confidence level, not a probability for a single interval in a frequentist sense), and option E is also an incorrect interpretation of what the confidence interval represents.

Answer:

C. We are 99% sure that the average amount of time spent studying among graduate students at this student's school is between 17.3 and 22.5 hours per week.