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).

BrandPrice ($)ScoreA18074B15069C9559D7056E7042F3524(a)

The estimated regression equation for this data is=23.398+0.306x,

wherex= price ($)andy= overall score.Does thettest indicate a significant relationship between price and the overall score? Use= 0.05.

State the null and alternative hypotheses.

H₀:₁0

H_a:₁= 0

H₀:₁= 0

H_a:₁0

H₀:₀= 0

H_a:₀0

H₀:₀0

H_a:₀= 0

H₀:₁0

H_a:₁< 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find thep-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

RejectH₀. We conclude that the relationship between price ($) and overall score is significant.

Do not rejectH₀. We conclude that the relationship between price ($) and overall score is significant.

Do not rejectH₀. We cannot conclude that the relationship between price ($) and overall score is significant.

RejectH₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b)

Test for a significant relationship using theFtest. Use= 0.05.

State the null and alternative hypotheses.

H₀:₁= 0

H_a:₁0

H₀:₀= 0

H_a:₀0

H₀:₁0

H_a:₁= 0

H₀:₁0

H_a:₁< 0

H₀:₀0

H_a:₀= 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find thep-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

RejectH₀. We conclude that the relationship between price ($) and overall score is significant.

Do not rejectH₀. We cannot conclude that the relationship between price ($) and overall score is significant.

RejectH₀. We cannot conclude that the relationship between price ($) and overall score is significant.

Do not rejectH₀. We conclude that the relationship between price ($) and overall score is significant.

(c)

Show the ANOVA table for these data. (Round yourp-value to three decimal places and all other values to two decimal places.)

Source

of VariationSum

of SquaresDegrees

of FreedomMean

SquareFp-valueRegressionErrorTotal