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 se confidence level. What does the confidence interval tell about the population of all college students in the state? 4.1, 31, 42, 4.7.3.0, 4.5, 3.5,47,44,40,41,3,6,34,38,39 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 late? Select the correct choice below and necessary, fa in the answer box(es) to complete your choice OA The results till nothing about the population of all college students in the state, since the sample is from only one university OB. We we confident that % of all students gave evaluation ratings between and (Round to one decimal place as needed) OC Wewe 98% confident that the interval from to actually contains the true mean evaluation rating. Round to one decimal places needed)

Answer 1

Solution:- Given that samples 4.1,3.1,4.2,4.7,3.0,4.5,3.5,4.7,4.4,4.0,4.1,3.6,3.4,3.8,3.9
X = 3.93, sd = 0.5354, n = 15, 98% Confidence interval

=> Confidence interval for the population mean = (3.57,4.23)

The provided sample mean is I = 3.93 and the sample standard deviation is s = 0.5354. The size of the sample is n = 15 and the required confidence level is 98%. The number of degrees of freedom are df = 15 - 1 = 14, and the significance level is a = 0.02. Based on the provided information, the critical t-value for a = 0.02 and df = 14 degrees of freedom is te = 2.624. The 98% confidence for the population mean u is computed using the following expression te xs CI=-tXs Therefore, based on the information provided, the 98 % confidence for the population mean is CI = 3.93 2.624 x 0.5354 .: 3.93 + V15 2.624 x 0.5354 V15 = (3.93 -0.363, 3.93 +0.363) = (3.567, 4.293)

=> option A.