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A researcher studies the relationship between SAT scores, the test-taker's family income (Income), and his/her grade point average (GPA). Data are collected from 24 students. She estimates the following model: (You may find it useful to reference the table.) Click here for the Excel Data File a-1. Estimate: SAT = Bo + B₁Income + B₂GPA + E. (Round your answers to 4 decimal places.) Predicted SAT Ho: B10; HA: B1₁ #0 ⒸHO: B₁ ≥ 0; HA: B₁ <0 ⒸHO: B₁ ≤0; HA: B₁>0 Income + a-2. Choose the hypotheses to determine whether Income is individually significant. GPA Test statistic a-3. Calculate the value of the test statistic. (Round your answer to 3 decimal places.)
a-4. Find the p-value. p-value < 0.01 0.01 s p-value < 0.025 0.025 s p-value < 0.05 0.05 s p-value < 0.10 p-value ≥ 0.10 a-5. At the 5% significance level, is income individually significant? Yes, since we reject the null hypothesis. No, since we reject the null hypothesis. O No, since we do not reject the null hypothesis. Yes, since we do not reject the null hypothesis.
a-9. At the 5% significance level, is GPA individually significant? Ⓒ Yes, since we reject the null hypothesis. O Yes, since we do not reject the null hypothesis No, since we reject the null hypothesis. No, since we do not reject the null hypothesis. b-1. Choose the hypotheses to determine whether Income and GPA are jointly significant. ⒸHO: B1 =B₂ = 0; HA: At least one Bj+0 ⒸHO: B₁=B₂ = 0; HA: At least one Bj<0 ⒸHO: B1-B₂=0; HA: At least one 3 > 0 b-2. Calculate the value of the test statistic. (Round your answer to 3 decimal places.) Test statistic
b-3. Find the p-value. p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 s p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10 b-4. At the 5% significance level, are income and GPA jointly significant? Yes, since the F-test is significant. Yes, since all t-tests are significant. Both answers are correct. c-1. Predict SAT Income is $80,000 and GPA is 3.5. (Round final answers to 2 decimal places.) Predicted SAT
c-2. If Income is $80,000 and GPA is 3.5. Construct a 95% prediction interval for the individual SAT score. (Round final answer to 2 decimal places.) Prediction interval to