The estimated regression equation for this data is 24.327759+0.316722x, where x-price ($) and yoverall score. Does the test indicate a significant relationship between price and the overall score? Use 0.05. State the null and alternative hypotheses. OM O "₂8-0 ⒸM₂-0 M₂0 OMA M₂₂0 ⒸM₂: A₂ 20 OM₂₁0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) What is your conclusion? Reject H. We conclude that the relationship between price ($) and overall score is significant. Do not reject H. We conclude that the relationship between price ($) and overall score is significant. Do not reject H₂, We cannot conclude that the relationship between price (5) and overall score is significant. Reject H. We cannot conclude that the relationship between price ($) and overall score is significant. Test for a significant relationship using the test. Use -0.05. State the null and alternative hypotheses. OM₂: ₂0 M₂A, OMA M₂₂-0 OMA H₂₂ O ⒸM₂: A=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.) What is your conclusion? Do not reject H₂, We cannot conclude that the relationship between price (5) and overall score is significant Reject H We cannot conclude that the relationship between price ($) and overall score is significant Reject H We conclude that the relationship between price ($) and overall score is significant. Do not reject M₂. We conclude that the relationship between price ($) and overall score is significant. Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.) Source Sum Degrees of Variation of Squares of Freedom Mean Square Regression Error p-value

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.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 87CR

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$### Analysis of Price and Overall Score Data for Stereo Headphones Consider the following data on price ($x$) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). | Brand | Price ($x$) | Score ($y$) | |-------|-------------|-----------| | A | 150 | 93 | | B | 160 | 76 | | C | 170 | 73 | | D | 190 | 80 | | E | 70 | 91 | | F | 35 | 46 | #### Estimating a Regression Equation The estimated regression equation for this data is: \[ \hat{y} = 34.27979 + 0.397292x \] where $ \hat{y} $ = predicted $y$ (the overall score), and $x$ = price. **Question: Does the test indicate a significant relationship between price and overall score? Use $\alpha = 0.05$.** ##### Hypothesis Testing for Slope ($ \beta_1 $) State the null and alternative hypotheses: \[ H_0: \beta_1 = 0 \] \[ H_a: \beta_1 \neq 0 \] 1. **Find the value of the test statistic.** (Round your answer to three decimal places.) Test statistic ($ t_{\text{stat}} $) = ________ 2. **Find the $ p $-value.** (Round your answer to four decimal places.) $ p $-value = ________ 3. **Conclusion:** - **Reject $H_0$**: We conclude that the relationship between price ($x$) and overall score is significant. - **Do not reject $H_0$**: We cannot conclude that the relationship between price ($x$) and overall score is significant. ##### Test for a Significant Relationship using the $F$ Test ($\alpha = 0.05$) State the null and alternative hypotheses: \[ H_0: \beta_1 = 0 \] \[ H_a: \beta_1 \neq 0 \]$

Transcribed Image Text:### Analysis of Price and Overall Score Data for Stereo Headphones Consider the following data on price ($x$) 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 ($x$) | Score ($y$) | |-------|-------------|-----------| | A | 150 | 93 | | B | 160 | 76 | | C | 170 | 73 | | D | 190 | 80 | | E | 70 | 91 | | F | 35 | 46 | #### Estimating a Regression Equation The estimated regression equation for this data is: \[ \hat{y} = 34.27979 + 0.397292x \] where $ \hat{y} $ = predicted $y$ (the overall score), and $x$ = price. **Question: Does the test indicate a significant relationship between price and overall score? Use $\alpha = 0.05$.** ##### Hypothesis Testing for Slope ($ \beta_1 $) State the null and alternative hypotheses: \[ H_0: \beta_1 = 0 \] \[ H_a: \beta_1 \neq 0 \] 1. **Find the value of the test statistic.** (Round your answer to three decimal places.) Test statistic ($ t_{\text{stat}} $) = ________ 2. **Find the $ p $-value.** (Round your answer to four decimal places.) $ p $-value = ________ 3. **Conclusion:** - **Reject $H_0$**: We conclude that the relationship between price ($x$) and overall score is significant. - **Do not reject $H_0$**: We cannot conclude that the relationship between price ($x$) and overall score is significant. ##### Test for a Significant Relationship using the $F$ Test ($\alpha = 0.05$) State the null and alternative hypotheses: \[ H_0: \beta_1 = 0 \] \[ H_a: \beta_1 \neq 0 \]

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