You may need to use the appropriate technology to answer this question. Consider the following data on price ($) and the

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You may need to use the appropriate technology to answer this question. Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). Brand A B C D E F Price ($) 180 150 95 70 70 35 Score 74 71 61 56 40 28
(a) The estimated regression equation for this data is ŷ= 25.133779 +0.298662x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use a = 0.05. State the null and alternative hypotheses. ⒸHo: Po * 0 H: Bo=Ọ Ho: P₁ 20 H₂: B₁ <0 O Ho: B₁ = 0 H₂: B₁ * 0 ọ Hoi noọ Ha: Po 0 #0 O Ho: P₁0 H₂: P₁=0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value= What is your conclusion? O Reject Ho. We conclude that the relationship between price ($) and overall score is significant. Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. Do not reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. Do not reject Ho. We conclude that the relationship between price ($) and overall score is significant.
(b) Test for a significant relationship using the F test. Use a = 0.05. State the null and alternative hypotheses. O Ho: B₁ * 0 H₂: P₁ = 0 O Ho: Po= 0 H: Bo #Ọ Ho: B₁ 20 H₂: P₁ <0 O Ho: P₁ = 0 H₂: P₁ #0 O Ho: Po * 0 Hai By O Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value= What is your conclusion? Do not reject Ho. We conclude that the relationship between price ($) and overall score is significant. Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. O Reject Ho. We conclude that the relationship between price ($) and overall score is significant. Do not reject Ho. We cannot 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: of Variation Regression Error Total Sum of Squares Degrees of Freedom Mean Square p-value