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 99​%

confidence level. What does the confidence interval tell about the population of all college students in the​ state?

4.0​, 3.0​,4.1​,4.8​, 3.0​ ,4.3​ ,3.7​ ,4.9​, 4.2​, 4.2​ ,4.1​ ,3.9 ​,3.4 ​,4.0​, 4.0

What is the confidence interval for the population mean μ​?

_____<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 99​% 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 99​% of all students gave evaluation ratings between _____ and______?

​(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.

Answer 1

Sample Size ,   n =    15
Sample Mean,    x̅ = ΣX/n =   3.973

sample std dev ,    s = √ [ Σ(X - X̄)²/(n-1)] =   0.540

degree of freedom=   DF=n-1=   14  

Level of Significance ,    α =    0.01

't value='   tα/2=   2.9768   [Excel formula =t.inv(α/2,df) ]
          
Standard Error , SE =   s/√n =   0.1395  
margin of error ,   E=t*SE =   0.415  

confidence interval is           
Interval Lower Limit=   x̅ - E =    3.558  
Interval Upper Limit=   x̅ + E =    4.389  

confidence interval for the population mean μ​ is 3.56<µ<4.39

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We are 99​% confident that the interval from 3.6 to 4.4  actually contains the true mean evaluation rating