The ACT is a standardized test that many high school students in the U.S. take i
ID: 433638 • 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% confidence interval for the mean GPA of students who have an ACT score of x p = 21. What is the upper bound of this interval, to three decimal places?
Hint: Use the confidence interval formula, not the prediction interval formula. The two formulas look very similar.
Explanation / Answer
Given data:
Interval confidence = 95%
Degree of freedom = 139
Random sample of students = 141
Critical Value = 1.977
Standard deviation = 2.844
Requried :
Upper Bound
Solution :
The ACT is a standardized test that many high school students in the U.S. order to apply for college. Measured by Grade point Average (GPA).
Prediction Interval = 95%
Freedom error = 139
Critical (t) = 1.977
Prediction Yhat = 2.402 + 0.027 +31
= 3.343
95% of Prediction Interval
= Yhat ± t(0.05,139) * Sqrt (MSE) * sqrt (1+1/n + (xo – x bar)2 / n-1) *sx2
= 3.343 ± 1.977 * sqrt (0.133644) * sqrt (1 +1/141 + (31 – 19.4)2/ 140-1) * (2.844)2
= 3.343 ± 1.977 * sqrt(0.1336) * 2.972
= 3.343±1.977 * 1.086
= 5.777
(or )
Upper Bound is 5.78
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