You may need to use the appropriate technology to answer this question. 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 ($) 2.22 72,000 2.27 48,000 2.57 72,000 2.59 62,000 2.77 86,000 2.85 98,000 3.12 133,000 3.35 130,000 3.66 157,000 3.68 162,000 (a) Develop a scatter diagram for these data with college GPA as the independent variable. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes down and right from (2.22, 122,000) to (3.68, 8,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes up and right from (2.22, 8,000) to (3.68, 122,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes down and right from (2.22, 162,000) to (3.68, 48,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes up and right from (2.22, 48,000) to (3.68, 162,000). The points are scattered moderately from the pattern. What does the scatter diagram indicate about the relationship between the two variables? The scatter diagram indicates a positive linear relationship between GPA and salary.The scatter diagram indicates no apparent relationship between GPA and salary. The scatter diagram indicates a nonlinear relationship between GPA and salary.The scatter diagram indicates a negative linear 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: ?0 ≠ 0 Ha: ?0 = 0H0: ?0 = 0 Ha: ?0 ≠ 0 H0: ?1 = 0 Ha: ?1 ≠ 0H0: ?1 ≥ 0 Ha: ?1 < 0H0: ?1 ≠ 0 Ha: ?1 = 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. Reject H0. There is not a significant statistical relationship between GPA and salary.Reject H0. There is a significant statistical relationship between GPA and salary. Do not reject H0. There is a significant statistical relationship between GPA and salary.Do not reject H0. There is not a significant statistical relationship between GPA and salary.

You may need to use the appropriate technology to answer this question. 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 ($) 2.22 72,000 2.27 48,000 2.57 72,000 2.59 62,000 2.77 86,000 2.85 98,000 3.12 133,000 3.35 130,000 3.66 157,000 3.68 162,000 (a) Develop a scatter diagram for these data with college GPA as the independent variable. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes down and right from (2.22, 122,000) to (3.68, 8,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes up and right from (2.22, 8,000) to (3.68, 122,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes down and right from (2.22, 162,000) to (3.68, 48,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes up and right from (2.22, 48,000) to (3.68, 162,000). The points are scattered moderately from the pattern. What does the scatter diagram indicate about the relationship between the two variables? The scatter diagram indicates a positive linear relationship between GPA and salary.The scatter diagram indicates no apparent relationship between GPA and salary. The scatter diagram indicates a nonlinear relationship between GPA and salary.The scatter diagram indicates a negative linear 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: ?0 ≠ 0 Ha: ?0 = 0H0: ?0 = 0 Ha: ?0 ≠ 0 H0: ?1 = 0 Ha: ?1 ≠ 0H0: ?1 ≥ 0 Ha: ?1 < 0H0: ?1 ≠ 0 Ha: ?1 = 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. Reject H0. There is not a significant statistical relationship between GPA and salary.Reject H0. There is a significant statistical relationship between GPA and salary. Do not reject H0. There is a significant statistical relationship between GPA and salary.Do not reject H0. There is not a significant statistical relationship between GPA and salary.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You may need to use the appropriate technology to answer this question.

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
2.27	48,000
2.57	72,000
2.59	62,000
2.77	86,000
2.85	98,000
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.

A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes down and right from (2.22, 122,000) to (3.68, 8,000). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes up and right from (2.22, 8,000) to (3.68, 122,000). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes down and right from (2.22, 162,000) to (3.68, 48,000). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes up and right from (2.22, 48,000) to (3.68, 162,000). The points are scattered moderately from the pattern.

What does the scatter diagram indicate about the relationship between the two variables?

The scatter diagram indicates a positive linear relationship between GPA and salary.The scatter diagram indicates no apparent relationship between GPA and salary. The scatter diagram indicates a nonlinear relationship between GPA and salary.The scatter diagram indicates a negative linear 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: ?₀ ≠ 0
H_a: ?₀ = 0H₀: ?₀ = 0
H_a: ?₀ ≠ 0 H₀: ?₁ = 0
H_a: ?₁ ≠ 0H₀: ?₁ ≥ 0
H_a: ?₁ < 0H₀: ?₁ ≠ 0
H_a: ?₁ = 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.

Reject H₀. There is not a significant statistical relationship between GPA and salary.Reject H₀. There is a significant statistical relationship between GPA and salary. Do not reject H₀. There is a significant statistical relationship between GPA and salary.Do not reject H₀. There is not a significant statistical relationship between GPA and salary.

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