Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. T

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Consider the following data on price ($) and the overall scorefor six stereo headphones tested by a certain magazine. The overallscore is based on sound quality and effectiveness of ambient noisereduction. Scores range from 0 (lowest) to 100 (highest).
(a)
The estimated regression equation for this data is
ŷ = 23.595318 + 0.314047x,
where x = price($) and y = overall score. Doesthe t test indicate a significant relationshipbetween price and the overall score? Use 𝛼 = 0.05.
State the null and alternative hypotheses.
H0: 𝛽1 ≠ 0Ha: 𝛽1 =0H0: 𝛽1 = 0Ha: 𝛽1 ≠ 0 H0: 𝛽1 ≥ 0Ha: 𝛽1 <0H0: 𝛽0 ≠ 0Ha: 𝛽0 =0H0: 𝛽0 = 0Ha: 𝛽0 ≠ 0
Find the value of the test statistic. (Round your answer tothree decimal places.)
Find the p-value. (Round your answer to fourdecimal places.)
p-value =
What is your conclusion?
Reject H0. We cannot conclude that therelationship between price ($) and overall score is significant.Donot reject H0. We conclude that therelationship between price ($) and overall score issignificant. Reject H0.We conclude that the relationship between price ($) and overallscore is significant.Do not reject H0. Wecannot conclude that the relationship between price ($) and overallscore is significant.
(b)
Test for a significant relationship usingthe F test. Use 𝛼 = 0.05.
State the null and alternative hypotheses.
H0: 𝛽1 ≥ 0Ha: 𝛽1 <0H0: 𝛽0 ≠ 0Ha: 𝛽0 =0 H0: 𝛽1 ≠ 0Ha: 𝛽1 =0H0: 𝛽1 = 0Ha: 𝛽1 ≠ 0H0: 𝛽0 =0Ha: 𝛽0 ≠ 0
Find the value of the test statistic. (Round your answer to twodecimal places.)
Find the p-value. (Round your answer to threedecimal places.)
p-value =
What is your conclusion?
Do not reject H0. We conclude that therelationship between price ($) and overall score issignificant.Reject H0. We cannot concludethat the relationship between price ($) and overall score issignificant. Do notreject H0. We cannot conclude that therelationship between price ($) and overall score issignificant.Reject H0. We conclude thatthe relationship between price ($) and overall score issignificant.
(c)
Show the ANOVA table for these data. (Roundyour p-value to three decimal places and all othervalues to two decimal places.)

Consider The Following Data On Price And The Overall Score For Six Stereo Headphones Tested By A Certain Magazine T 1 (115.09 KiB) Viewed 13 times

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). Brand Price ($) A B с D E F Ho: P₁ = 0 H₂: B₁ * 0 O Ho: B₁ 20 H₂: B₁ <0 180 ọ Hoi Boto 150 Ha: Bo = 0 95 70 70 35 Score 74 73 61 (a) The estimated regression equation for this data is ŷ = 23.595318+ 0.314047x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05. 58 State the null and alternative hypotheses. O Ho: B₁ * 0 Ha: P₁ = 0 38 26 ọ Hoi Bo=0 Ha: Po 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? O Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. O Do not reject Ho. We 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.
(b) Test for a significant relationship using the F test. Use α = 0.05. State the null and alternative hypotheses. O Ho: B₁ ≥ 0 Ha: B₁ <0 ọ Hoi Do#0 Ha: Po = 0 O Ho: B₁ * 0 H₂: P₁ = 0 Ho: B₁ = 0 H₂: B₁ * 0 ọ Hoi Bo = 0 Ha: Po 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 Do not reject Ho. We conclude that the relationship between price ($) and overall score is significant. O Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. O Do not 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. (c) Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.) Mean Square Source of Variation Regression Error Total Sum Degrees of Squares of Freedom p-value