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
What does the confidence interval tell about the population of all college students in the state?
?
What is the confidence interval for the population mean
?
(Round to two decimal places as needed)
What does the confidence interval tell about the population of all college students in the state?
What is the confidence interval for the population mean
Ask by Ray Newton. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The confidence interval for the population mean
is
.
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
The Deep Dive
To construct a confidence interval for the population mean
based on the given student evaluation ratings, we first need to calculate the mean and standard deviation of the sample data.
The ratings provided are:
.
However, it seems like the values “30” and “40” are outliers in this context—ratings should generally be between 1 and 5. So let’s focus on the plausible ratings first:
-
Remove the outliers:
Ratings used:. -
Calculate the sample mean (
): -
Calculate the sample standard deviation (s):
-
Determine the sample size (n = 12) and the critical value for a 95% confidence interval, which for a two-tailed t-distribution with
degrees of freedom (11 df) is approximately 2.201. -
Calculate the standard error (SE):
-
Construct the confidence interval:This results in:
Thus, the confidence interval for the population mean
is:
(Rounded to two decimal places as needed.)