The ACT is a standardized test that many high school students in the U.S. take i
ID: 3229237 • 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 x0 = 13. What is the upper bound of this interval, to two decimal places?
Hint: Use the confidence interval formula, not the prediction interval formula. The two formulas are very similar, but the confidence interval formula leaves off the "1+" under the square root.
Regression Statistics Multiple R 0.206754254 R Square 0.042747321 Adjusted R Square 0.035860611 Standard Error 0.365573763 Observations 141 ANOVA df SS MS F Significance F Regression 1 0.829558763 0.829559 6.20722 0.013899275 Residual 139 18.57654053 0.133644 Total 140 19.40609929 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 2.402979486 0.264202725 9.095211 8.8E-16 1.880603742 2.925355229 ACT 0.027063973 0.01086283 2.491429 0.013899 0.005586227 0.048541719Explanation / Answer
Formula:
predicted value=y_hat=2.403+.027*13 2.754 Std error for CI of this prediction= =sqrt[(MSE)*[1/N+(X-X_MEAN)^2/((n-1)*VarX))] 0.05775 t-stat for 95% CI= 2.265942 95% CI: Lower bound= 2.623141 upper bound= 2.884859Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.