Do students with higher college grade point averages (GPAs) earn more than those graduates with lower GPAs?† Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary ($) 2.22 72,000 2.29 48,000 2.57 72,000 2.59 62,000 2.77 86,000 2.85 96,000 3.12 133,000 3.35 130,000 3.66 157,000 3.68 162,000 (a) Develop a scatter diagram for these data with college GPA as the independent variable What does the scatter diagram indicate about the relationship between the two variables? (A) The scatter diagram indicates a negative linear relationship between GPA and salary. (B) The scatter diagram indicates a nonlinear relationship between GPA and salary. (C) The scatter diagram indicates a positive linear relationship between GPA and salary. (D) The scatter diagram indicates no apparent relationship between GPA and salary. (b) Use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college GPA. (Let x = GPA, and let y = salary (in $). Round your numerical values to the nearest integer.) ŷ = ______ (c) At the 0.05 level of significance, does there appear to be a significant statistical relationship between the two variables? (Use the F test.) State the null and alternative hypotheses. H0: β1 = 0 Ha: β1 ≠ 0 H0: β0 = 0 Ha: β0 ≠ 0 H0: β1 ≥ 0 Ha: β1 < 0 H0: β0 ≠ 0 Ha: β0 = 0 H0: β1 ≠ 0 Ha: β1 = 0 Find the value of the test statistic. (Round your answer to two decimal places.) = ____ Find the p-value. (Round your answer to three decimal places.) p-value = _____ State your conclusion. (A) Do not reject H0. There is not a significant statistical relationship between GPA and salary. (B) Reject H0. There is a significant statistical relationship between GPA and salary. (C) Do not reject H0. There is a significant statistical relationship between GPA and salary. (D) Reject H0. There is not a significant statistical relationship between GPA and salary.
Do students with higher college grade point averages (GPAs) earn more than those graduates with lower GPAs?† Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary ($) 2.22 72,000 2.29 48,000 2.57 72,000 2.59 62,000 2.77 86,000 2.85 96,000 3.12 133,000 3.35 130,000 3.66 157,000 3.68 162,000 (a) Develop a scatter diagram for these data with college GPA as the independent variable What does the scatter diagram indicate about the relationship between the two variables? (A) The scatter diagram indicates a negative linear relationship between GPA and salary. (B) The scatter diagram indicates a nonlinear relationship between GPA and salary. (C) The scatter diagram indicates a positive linear relationship between GPA and salary. (D) The scatter diagram indicates no apparent relationship between GPA and salary. (b) Use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college GPA. (Let x = GPA, and let y = salary (in $). Round your numerical values to the nearest integer.) ŷ = ______ (c) At the 0.05 level of significance, does there appear to be a significant statistical relationship between the two variables? (Use the F test.) State the null and alternative hypotheses. H0: β1 = 0 Ha: β1 ≠ 0 H0: β0 = 0 Ha: β0 ≠ 0 H0: β1 ≥ 0 Ha: β1 < 0 H0: β0 ≠ 0 Ha: β0 = 0 H0: β1 ≠ 0 Ha: β1 = 0 Find the value of the test statistic. (Round your answer to two decimal places.) = ____ Find the p-value. (Round your answer to three decimal places.) p-value = _____ State your conclusion. (A) Do not reject H0. There is not a significant statistical relationship between GPA and salary. (B) Reject H0. There is a significant statistical relationship between GPA and salary. (C) Do not reject H0. There is a significant statistical relationship between GPA and salary. (D) Reject H0. There is not a significant statistical relationship between GPA and salary.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 81E
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Do students with higher college grade point averages (GPAs) earn more than those graduates with lower GPAs?† Consider the following hypothetical college GPA and salary data (10 years after graduation).
| GPA | Salary ($) |
|---|---|
| 2.22 | 72,000 |
| 2.29 | 48,000 |
| 2.57 | 72,000 |
| 2.59 | 62,000 |
| 2.77 | 86,000 |
| 2.85 | 96,000 |
| 3.12 | 133,000 |
| 3.35 | 130,000 |
| 3.66 | 157,000 |
| 3.68 | 162,000 |
(a) Develop a scatter diagram for these data with college GPA as the independent variable
What does the scatter diagram indicate about the relationship between the two variables?
(A) The scatter diagram indicates a negative linear relationship between GPA and salary.
(B) The scatter diagram indicates a nonlinear relationship between GPA and salary.
(C) The scatter diagram indicates a positive linear relationship between GPA and salary.
(D) The scatter diagram indicates no apparent relationship between GPA and salary.
(b) Use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college GPA. (Let x = GPA, and let y = salary (in $). Round your numerical values to the nearest integer.)
ŷ = ______
(c) At the 0.05 level of significance, does there appear to be a significant statistical relationship between the two variables? (Use the F test.)
State the null and alternative hypotheses.
H0: β1 = 0
Ha: β1 ≠ 0
Ha: β1 ≠ 0
H0: β0 = 0
Ha: β0 ≠ 0
Ha: β0 ≠ 0
H0: β1 ≥ 0
Ha: β1 < 0
Ha: β1 < 0
H0: β0 ≠ 0
Ha: β0 = 0
Ha: β0 = 0
H0: β1 ≠ 0
Ha: β1 = 0
Ha: β1 = 0
Find the value of the test statistic. (Round your answer to two decimal places.) = ____
Find the p-value. (Round your answer to three decimal places.)
p-value = _____
State your conclusion.
(A) Do not reject H0. There is not a significant statistical relationship between GPA and salary.
(B) Reject H0. There is a significant statistical relationship between GPA and salary.
(C) Do not reject H0. There is a significant statistical relationship between GPA and salary.
(D) Reject H0. There is not a significant statistical relationship between GPA and salary.
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