Answer Happy

You may need to use the appropriate technology to answer this question. Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highes Brand Price ($) A B с D E F OH: B₁₁=0 Hiß #0 OH: B₂ #0 H₂:₁ = 0 180 OH: B₂ 20 H₂: B₁ <0 150 95 70 70 35 Score 78 71 63 58 (a) The estimated regression equation for this data is ý = 24.060201 + 0.319398x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use a = 0.05. State the null and alternative hypotheses. OH: #0 H₁₂ :B₁₂ = 0 38 28 OH₁: B₁ = 0 H_₂: B₁ #0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? O Reject H. We cannot conclude that the relationship between price ($) and overall score is significant. O Do not reject H. We conclude that the relationship between price ($) and overall score is significant. O Reject H. We conclude that the relationship between price ($) and overall score is significant. O Do not reject H. We cannot conclude that the relationship between price ($) and overall score is significant.
(b) Test for a significant relationship using the F test. Use a = 0.05. State the null and alternative hypotheses. OH: B₁₂ #0 H₁₂ : B = 0 OH: B₂ #0 H₁₂ : P₁ = 0 OH: B₂ 20 H₂: P₂ <0 OH₁₂ : B₁ = 0 H₂: A₁ = 0 OHO: Bo = 0 H₁₂ : A = 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = What is your conclusion? O Reject H. We cannot conclude that the relationship between price ($) and overall score is significant. O Do not reject H. We conclude that the relationship between price ($) and overall score is significant. O Do not reject H₁. We cannot conclude that the relationship between price ($) and overall score is significant. O Reject H. We conclude that the relationship between price ($) and overall score is significant. (c) Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.) Source Degrees of Freedom of Variation Regression Error Total Sum of Squares Mean Square F p-value