Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).| Brand | Price ($) | Score ||-------|-----------|-------|| A | 180 | 76 || B | 150 | 69 || C | 95 | 59 || D | 70 | 56 || E | 70 | 40 || F | 35 | 24 |(a) The estimated regression equation for this data is $ \hat{y} = 21.926421 + 0.320736x $, where $ x $ = price ($) and $ y $ = overall score. Does the t-test indicate a significant relationship between price and the overall score? Use $ \alpha = 0.05 $.State the null and alternative hypotheses.- $ H_0: \beta_1 = 0 $- $ H_a: \beta_1 \neq 0 $ **Statistical Analysis Result:**1. **Test Statistic:** - Value: 2.988 (Incorrect)2. **P-value:** - Value: 0.0404 (Incorrect)3. **Conclusion Options:** - Do not reject $ H_0 $: We cannot conclude that the relationship between price (\$) and overall score is significant. - Reject $ H_0 $: We cannot conclude that the relationship between price (\$) and overall score is significant. - **Reject $ H_0 $: We conclude that the relationship between price (\$) and overall score is significant.** (Correct choice) - Do not reject $ H_0 $: We conclude that the relationship between price (\$) and overall score is significant.**Graph/Diagram Explanation:**The image provides an interface for testing hypotheses about the relationship between price and overall score. The options indicate a decision-making process based on statistical values, with the correct conclusion highlighted.

Answered: Find the value of the test statistic.…

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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$Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). | Brand | Price ($) | Score | |-------|-----------|-------| | A | 180 | 76 | | B | 150 | 69 | | C | 95 | 59 | | D | 70 | 56 | | E | 70 | 40 | | F | 35 | 24 | (a) The estimated regression equation for this data is $ \hat{y} = 21.926421 + 0.320736x $, where $ x $ = price ($) and $ y $ = overall score. Does the t-test indicate a significant relationship between price and the overall score? Use $ \alpha = 0.05 $. State the null and alternative hypotheses. - $ H_0: \beta_1 = 0 $ - $ H_a: \beta_1 \neq 0 $$

Transcribed Image Text:Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). | Brand | Price ($) | Score | |-------|-----------|-------| | A | 180 | 76 | | B | 150 | 69 | | C | 95 | 59 | | D | 70 | 56 | | E | 70 | 40 | | F | 35 | 24 | (a) The estimated regression equation for this data is $ \hat{y} = 21.926421 + 0.320736x $, where $ x $ = price ($) and $ y $ = overall score. Does the t-test indicate a significant relationship between price and the overall score? Use $ \alpha = 0.05 $. State the null and alternative hypotheses. - $ H_0: \beta_1 = 0 $ - $ H_a: \beta_1 \neq 0 $