Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ratings were obtained at one university in a s What does the confidence interval tell about the population of all college students in the state? \( 3.6,3.0,4.0,4.6,3.1,4.5,3.4,4.4,4.6,4.0,4.6,3.7,3.0,3.7,4.0 \), What is the confidence interval for the population mean \( \mu \) ? \( 3.43<\mu<4.33 \) (Round to two decimal places as needed.) What does the confidence interval tell about the population of all college students in the state? Select the correct choice below and, if necessan A. We are confident that \( 99 \% \) of all students gave evaluation ratings between \( \square \) and \( \square \). (Round to one decimal place as needed.) Che results tell nothing about the population of all college students in the state, since the sample is from only one university. (Re are \( 99 \% \) confident that the interval from \( \square \) to \( \square \) actually contains the true mean evaluation rating. (Roce as needed.)
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The confidence interval suggests that we can be quite sure—around 99%—that the true mean evaluation rating \( \mu \) for all college students in the state falls between 3.43 and 4.33. This implies that, on average, students from various universities likely share similar ratings of course quality, though individual experiences may vary. This statistical estimate gives a fun twist on how feedback from one university can resonate across a larger population! When considering confidence intervals, one common mistake students make is thinking that 99% confidence means 99% of the individual ratings fall between the endpoints. In reality, it’s about the overall mean—the average evaluation ratings of all students—falling within that range. So next time you crunch numbers, remember: confidence intervals are about predicting the average, not the individual student scores!
