Answered: The following data on price ($) and the…

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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1a. Does the t test indicate a significant relationship between price and the overall score?

Compute the value of the t test statistic. Use x=0.05

$**Educational Website Transcription: Analysis of Price and Score Data for Stereo Headphones** --- ### Introduction An analysis was conducted on price ($) and the overall score for six stereo headphones based on Consumer Reports. The regression equation is: \[ \hat{y} = 23.002 + 0.313x \] ### Data Table | Brand | Price ($) | Score | |-----------------|-----------|-------| | Bose | 190 | 78 | | Skullcandy | 150 | 71 | | Koss | 85 | 61 | | Phillips/O'Neill| 80 | 56 | | Denon | 80 | 40 | | JVC | 35 | 26 | ### Statistical Analysis #### a. t-Test Analysis - **Objective:** Determine if there's a significant relationship between price and the overall score. - **t-Statistic Calculation:** Compute using α = 0.05. \[ t = \text{(to 2 decimal places)} \] - **p-value Determination:** Use Table 2 of Appendix B. \[ \text{p-value is between 0.02 and 0.05} \] - **Conclusion:** At α = 0.05, there is a significant relationship between price and overall score. #### b. F-Test Analysis - **Objective:** Test for a significant relationship using the F test. \[ \text{p-value is between 0.025 and 0.05} \] - **Conclusion:** With α = 0.05, we reject $ H_0: \beta_1 $ is equal to zero, indicating a significant relationship. #### c. ANOVA Table - **Note:** Round answers to three decimal places, but avoid rounding intermediate calculations. --- This analysis helps determine how price influences headphone scores, guiding consumers and manufacturers in understanding product value.$

Transcribed Image Text:**Educational Website Transcription: Analysis of Price and Score Data for Stereo Headphones** --- ### Introduction An analysis was conducted on price ($) and the overall score for six stereo headphones based on Consumer Reports. The regression equation is: \[ \hat{y} = 23.002 + 0.313x \] ### Data Table | Brand | Price ($) | Score | |-----------------|-----------|-------| | Bose | 190 | 78 | | Skullcandy | 150 | 71 | | Koss | 85 | 61 | | Phillips/O'Neill| 80 | 56 | | Denon | 80 | 40 | | JVC | 35 | 26 | ### Statistical Analysis #### a. t-Test Analysis - **Objective:** Determine if there's a significant relationship between price and the overall score. - **t-Statistic Calculation:** Compute using α = 0.05. \[ t = \text{(to 2 decimal places)} \] - **p-value Determination:** Use Table 2 of Appendix B. \[ \text{p-value is between 0.02 and 0.05} \] - **Conclusion:** At α = 0.05, there is a significant relationship between price and overall score. #### b. F-Test Analysis - **Objective:** Test for a significant relationship using the F test. \[ \text{p-value is between 0.025 and 0.05} \] - **Conclusion:** With α = 0.05, we reject $ H_0: \beta_1 $ is equal to zero, indicating a significant relationship. #### c. ANOVA Table - **Note:** Round answers to three decimal places, but avoid rounding intermediate calculations. --- This analysis helps determine how price influences headphone scores, guiding consumers and manufacturers in understanding product value.

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