Question

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 state. Construct a confidence interval using a 95% confidence level. What does the confidence interval tell about the population of all college students in the state? 3.8, 2.9, 4.0, 4.5, 3.1, 4.4, 3.5, 4.8, 4.3, 3.9, 4.5, 3.5, 3.2, 3.9, 4.1

What is the confidence interval for the population mean µ? << (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 necessary, fill in the answer box(es) to complete your choice.
A. We are 95% confident that the interval from to actually contains the true mean evaluation rating. (Round to one decimal place as needed.)
B. We are confident that 95% of all students gave evaluation ratings between (Round to one decimal place as needed.)
C. The results tell nothing about the population of all college students in the state, since the sample is from only one university. and

Answer 1

The confidence interval for the population mean µ is (3.56, 4.24) based on the given data. The correct interpretation of the confidence interval is: A. We are 95% confident that the interval from 3.56 to 4.24 actually contains the true mean evaluation rating.

Step-by-step explanation:

To find the confidence interval for the population mean µ, you can use the formula:

`\[ \text{Confidence Interval} = \bar{x} \pm z \left( (s)/(√(n)) \right) \]`

Given the ratings data: 3.8, 2.9, 4.0, 4.5, 3.1, 4.4, 3.5, 4.8, 4.3, 3.9, 4.5, 3.5, 3.2, 3.9, 4.1, where
`\(\bar{x}\)` is the sample mean,
`\(s\)` is the sample standard deviation,
`\(n\)` is the sample size, and
`\(z\)` is the z-score corresponding to a 95% confidence level.

First, calculate the sample mean
`\(\bar{x}\)` and sample standard deviation
`\(s\)` . Then, determine the z-score for a 95% confidence level. After that, use these values to calculate the confidence interval.

Interpreting the confidence interval: A 95% confidence level implies that if we were to take many samples and construct confidence intervals in the same way, approximately 95% of these intervals would contain the true population mean.

Therefore, we can be 95% confident that the true mean evaluation rating of all college students in the state lies between 3.56 and 4.24. This interval provides insight into the likely range within which the population mean rating would fall based on the sample data collected from one university in the state.