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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, 3.1, 3.8, 4.5, 3.0, 4.4, 3.5, 4.6, 4.2, 4.1, 4.6, 3.9, 3.5, 4.0, 3.9
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, 3.1, 3.8, 4.5, 3.0, 4.4, 3.5, 4.6, 4.2, 4.1, 4.6, 3.9, 3.5, 4.0, 3.9
Given Information:population size = N = 15Confidence level = 90%Required Information:confidence interval = ?Answer:confidence interval = (3.88, 4.26)Step-by-step explanation:The confidence interval can be found byconfidence interval = μ ± (tα/2)*ο/√NWhere μ is the mean of population, ο is standard deviation of population, N is the population size and tα/2 is the t score corresponding toα = 100% - 99%α = 1%α = 0.01degree of freedom = N - 1degree of freedom = 15 - 1degree of freedom = 14From the t-table, the t-score for 99% confidence level and 14 DoF istα/2 = 2.977The mean of the population is given byMean = μ = ∑(xi)/Nμ = (4.0+3.1+3.8+4.5+3.0+4.4+3.5+4.6+4.2+4.1+4.6+3.9+3.5+4.0+3.9)/15μ = 61.05/15μ = 4.07The standard deviation of the population is given byο = √∑(xi - μ)²/(N - 1)ο = 0.25confidence interval = μ ± (tα/2)*ο/√Nconfidence interval = 4.07 ± (2.977)*0.25/√15confidence interval = 4.07 ± 0.19upper limit = 4.07 + 0.19 = 4.26lower limit = 4.07 - 0.19 = 3.88confidence interval = (3.88, 4.26)We are 90% confident that the student evaluation ratings of courses are from 3.88 to 4.26 that were obtained at one university in a state....