The ACT is a standardized test that many high school students in the U.S. take i
ID: 3227702 • Letter: T
Question
The ACT is a standardized test that many high school students in the U.S. take in order to apply for college (the other major admissions test is the SAT). The purpose of any standardized admissions test is to allow the institution at which the student is applying to predict how a student would perform academically, as measured by grade point average (GPA). Of course, many other criteria are considered by admissions committees, such as high school GPA and involvement in extracurricular activities, but we won't get into those here. The dean of a college of business at a medium-sized regional university is interested in examining the relationship between ACT scores and GPAs of students in the college. After taking a random sample of 141 students, he performs a regression analysis using Excel and gets the output below: The dean wants to create a 95% prediction interval for the GPA of a student who has an ACT score of x_0 = 31. What is the upper bound of this interval, to two decimal places? You will need to use the fact that the average ACT score X = is 19.4, with a standard deviation of 4.5. Use three decimal places for all calculations up to the answer.Explanation / Answer
For 95% prediction interval ,degree of freedom error=139 and critical t=1.977
Prediction yhat=2.402979486+0.027063973*31=3.241962649
95% prediction interval =yhat± t(0.05,139)*sqrt(MSE)*sqrt(1+1/n+(x0-xbar)2/(n-1)sx2)
=3.241962649 ±1.977 *sqrt(0.133644)*sqrt(1+1/141+(31-19.4)2/(140-1)*4.52)
=(-0.039164897 6.523090195)
So upper bound=6.52
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