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). Scores on the ACT range from 1 to 36 in one point increments. The dean of a college of business 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: Regression Statistics Multiple R 0.206754254 R Square 0.042747321 Adjusted R Square 0.035860611 Standard Error 0.365573763 Observations 141 ANOVA Significance F 0.013899275 6.20722 Regression Residual Total 1 139 140 SS MS 0.829558763 0.829559 18.57654053 0.133644 19.40609929 Intercept ACT Coefficients Standard Error t Stat P-value 2.402979486 0.264202725 9.095211 8.8E-16 0.027063973 0.01086283 2.491429 0.013899 Lower 95% Upper 95% 1.880603742 2.925355229 0.005586227 0.048541719 Use the output above to test at the a = 0.05 level of significance whether ACT is potentially useful for predicting GPA by filling in the blanks below. Use the p-value approach to make your conclusion. Report numbers to three (3) decimal places. Hint: There is nothing to calculate here; the output has everything you need. 1). Hypotheses Ho: B1 = vs. H1: B1 2). Test Statistic (Report to three (3) decimal places.) t = 3). P-Value (Report to three (3) decimal places.) p-value = 4). Conclusion Because the p-value is (less/greater) than , the dean can (reject/fail to reject) the null hypothesis. Therefore, the dean (can/cannot) conclude that ACT score is potentially useful for predicting GPA.

Answer 1

ili we want to test that, Act is signilicciata 1 Ho: B=0 vis Hall B. to 2 Test Stati-zic, t = ? from table "estate vale for ACT. t=2.4914 29 ~ 2.491 2.491 3) P-vane = ? From table, "p-value" for ACT P-vane = 0.0138,99 0.0141 0.014 4) a= 0.05; Reject Ho, if p-vale 20.05 Here P-valle = 0.014 0.05ouq we reject: Ho. u Berowe. the p-vale is less than 0.05 the dean can reject the nuil Hupo. Therefore, the dean can conclude treet Act score is potentially Well Predicding GPA oft