Question

Lieted below are student evaluation ratings of courses, where a rating of 5 is for "oxcelent." The ratings were obtained at ene univortity in a stabe. Conatruct a contldence interval uaing a s9y confidence level. What doos the oonfidence inlerval tell about the population of all college stidents in the state? 3.7,3.2,3.8,4.6,3,1,4,1,3,4,4.4,4.2,4.4,4.3,3,5.3.3,39,4.0= What is the confidence interval for the population mean μ ? (Reand to two deoimal piaces as needed.) What does the confldenoe interval tell about the popalation of all cologe students in the state? Select the comect choicu bolow and, if nicessur, fa in the annaur tariasi to comeinte your choice A. We are confident that 90% of all students gave oviluation ratings between and (Round to ono docimal place at needed) B. The rowits tell nothing about the populstion of all colege students in the stave, since the sample is from enly ane univerity. c. We are 99x contident that the interval from. to actualy contains the true masa evaluation rating. (Round to one docimal placo as neodod)

Answer 1

A confidence interval represents a range likely to contain the population parameter, not a percentage of data. A 99% confidence interval signifies a high level of confidence in the range, but the sample must be representative. The 90% confidence interval is constructed using the sample mean and standard deviation and is narrower than a 95% interval.

Step-by-step explanation:

Understanding Confidence Intervals

A confidence interval is a range of values derived from sample data that is likely to contain the true population parameter (like a population mean) with a certain level of confidence. It is not correct to say that a confidence interval contains a certain percentage of the data from a sample. Instead, it means that if we were to take many samples and build confidence intervals for each of them, a certain percentage of these intervals would contain the true population parameter.

In this particular case, a 99% confidence interval would imply that we are 99% confident that the range calculated from the sample data includes the true mean rating of all college courses in the state. However, since the sample is taken from only one university, the confidence interval might not be representative of all students across different universities in the state.

Calculating a Confidence Interval

When constructing a confidence interval, one would use the sample mean, the standard deviation (if available), and the size of the sample to determine the margin of error and eventually the interval itself. For example, a 90% confidence interval would be narrower than a 95% confidence interval because a lower confidence level implies a smaller margin of error, accepting a higher risk that the interval might not contain the true mean.