We want to estimate the mean sleep time (in hours per night) in the population o

Question

We want to estimate the mean sleep time (in hours per night) in the population of all STAT 1350 students. We take a random sample of 100 STAT 1350 students and use their sample mean sleep time to construct a 95% confidence interval. Which of the following interpretations of this interval are correct, and WHY? (IMPORTANT: Please note that more than one of the following interpretations may be correct!) We can be 95% confident the interval contains the true population mean. There is a 95% chance the sample mean will fall within the confidence interval. 95% of the students in the population will have sleep times that fall in the interval we constructed. If we take another random sample of 100 STAT 1350 students, there is a 95% chance that its sample mean would fall in the interval we constructed (i.e., the interval constructed based on the first sample of data). If we repeatedly took random samples of college students and generated a 95% confidence interval based on each sample mean, then, in the long run, 95% of the constructed confidence intervals would contain the true population mean.

Explanation / Answer

Interpretations 1 and 5 are correct

this is by the definition of confidence interval

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