Question

Data was collected from 252 students on the number of hours they slept the previous night. the 95% confidence interval created by minitab was: (7.34, 7.71). determine if each of the following statements is a correct or incorrect interpretation of the interval.

_________95% of students slept between 7.34 and 7.71 hours the previous night.

Answer 1

The statement that 95% of students slept between 7.34 and 7.71 hours is incorrect; the confidence interval suggests where the true population mean likely falls.

Step-by-step explanation:

The statement '95% of students slept between 7.34 and 7.71 hours the previous night' is incorrect. A 95% confidence interval represents the range within which we are 95% confident that the true mean of a population parameter lies, not the range of individual values.

Instead, the correct interpretation is that we are 95% confident that the average number of hours slept by all students falls between 7.34 and 7.71 hours. It does not provide information about the individual sleep durations of each student in the study.

The correct interpretation of the 95% confidence interval (7.34, 7.71) is that there is a 95% probability that the true population mean of the number of hours students slept the previous night falls between 7.34 and 7.71 hours.

This means that we can be confident that most students in the population slept between 7.34 and 7.71 hours the previous night.