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 95% 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.
o a. graduate students at this students school study between 17.3 and 22.5 hours per week 95% of all weeks during the year.
o b. approximately 95% 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.
o c. we are 95% 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.
o d. there is a 95% 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.
o e. at this students school 95% of all graduate students study between 17.3 and 22.5 hours per week on average

Explanation:

Step1: Understand Confidence Interval Interpretation

A \(95\%\) confidence interval \((17.3,22.5)\) for the population mean (average time spent studying among all graduate students at the school) means that if we were to take many random samples and construct confidence intervals, about \(95\%\) of those intervals would contain the true population mean.

Step2: Analyze Each Option

• Option A: A confidence interval is about the population mean, not about \(95\%\) of the individuals. So, saying " \(95\%\) of all weeks during the year graduate students at this student's school study between \(17.3\) and \(22.5\) hours per week" is incorrect.
• Option B: Confidence intervals are for the population mean, not for sample means. Saying "random samples of graduate students from this school will give a mean number of hours studied per week between \(17.3\) and \(22.5\)" is wrong.
• Option C: A \(95\%\) confidence interval does not mean \(99\%\) certainty. The confidence level is \(95\%\), so this option is incorrect.
• Option D: The confidence interval is about the population (all graduate students at the school), not about a \(95\%\) chance for the population. The interpretation of confidence intervals is in terms of the long - run frequency of intervals containing the population parameter.
• Option E: A \(95\%\) confidence interval \((17.3,22.5)\) for the population mean (average time spent studying by all graduate students at the school) is correctly interpreted as "At this student's school \(95\%\) of all graduate students study between \(17.3\) and \(22.5\) hours per week on average". This is the correct interpretation of a confidence interval for the population mean.

Answer:

E. At this student's school \(95\%\) of all graduate students study between \(17.3\) and \(22.5\) hours per week on average.