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 toanswer this question.
Consider the following data on price ($) and the overall scorefor six stereo headphones tested by a certain magazine. The overallscore is based on sound quality and effectiveness of ambient noisereduction. Scores range from 0 (lowest) to 100 (highest).
(a)
The estimated regression equation for this data is
ŷ = 26.204013 + 0.287960x,
where x = price($) 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: 𝛽0 = 0Ha: 𝛽0 ≠ 0H0: 𝛽0 ≠ 0Ha: 𝛽0 =0 H0: 𝛽1 ≠ 0Ha: 𝛽1 =0H0: 𝛽1 = 0Ha: 𝛽1 ≠ 0H0: 𝛽1 ≥ 0Ha: 𝛽1 < 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 conclude that therelationship between price ($) and overall score is significant.Donot reject H0. We cannot conclude that therelationship between price ($) and overall score issignificant. Do notreject H0. We conclude that therelationship between price ($) and overall score issignificant.Reject H0. We cannot concludethat the relationship between price ($) and overall score issignificant.
(b)
Test for a significant relationship usingthe F test. Use 𝛼 = 0.05.
State the null and alternative hypotheses.
H0: 𝛽0 = 0Ha: 𝛽0 ≠ 0H0: 𝛽1 =0Ha: 𝛽1 ≠ 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?
Reject H0. We conclude that therelationship between price ($) and overall score is significant.Donot reject H0. We conclude that therelationship between price ($) and overall score issignificant. Do notreject H0. We cannot conclude that therelationship between price ($) and overall score issignificant.Reject H0. We cannot concludethat the relationship between price ($) 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.)