Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).BrandPrice ($)ScoreA18078B15073C9563D7058E7040F3524(a) The estimated regression equation for this data is ŷ = 22.054 + 0.339x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use ? = 0.05.State the null and alternative hypotheses.??-H0: ?0 = 0Ha: ?0 ≠ 0-H0: ?1 = 0Ha: ?1 ≠ 0 -H0: ?0 ≠ 0Ha: ?0 = 0-H0: ?1 ≠ 0Ha: ?1 = 0-H0: ?1 ≥ 0Ha: ?1 < 0Find the value of the test statistic. (Round your answer to three decimal places.)test statistic=??Find the p-value. (Round your answer to four decimal places.)p-value = ??What is your conclusion?-Do not reject H0. We conclude that the relationship between price ($) and overall score is significant.-Reject H0. We conclude that the relationship between price ($) and overall score is significant. - Reject H0. We cannot conclude that the relationship between price ($) and overall score is significant.-Do not reject H0. We cannot conclude that the relationship between price ($) and overall score is significant.(b)Test for a significant relationship using the F test. Use ? = 0.05.State the null and alternative hypotheses.-H0: ?1 ≠ 0Ha: ?1 = 0-H0: ?0 ≠ 0Ha: ?0 = 0 - H0: ?0 = 0Ha: ?0 ≠ 0-H0: ?1 = 0Ha: ?1 ≠ 0-H0: ?1 ≥ 0Ha: ?1 < 0Find the value of the test statistic. (Round your answer to two decimal places.)Test statistic=??Find the p-value. (Round your answer to three decimal places.)p-value = ??What is your conclusion?-Do not reject H0. We conclude that the relationship between price ($) and overall score is significant.-Do not reject H0. We cannot conclude that the relationship between price ($) and overall score is significant. - Reject H0. We cannot conclude that the relationship between price ($) and overall score is significant.-Reject H0. 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.)Sourceof VariationSumof SquaresDegreesof FreedomMeanSquareFp-valueRegression?????Error??? Total??

applying regression: a) null hypothesis:Ho: β1 = 0 Alternate Hypothesis: Ha: β1 ≠ 0…

Answered: Consider the following data on price…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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	Price ($)	Score
A	180	78
B	150	73
C	95	63
D	70	58
E	70	40
F	35	24

(a) The estimated regression equation for this data is

ŷ = 22.054 + 0.339x,

where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use ? = 0.05.

State the null and alternative hypotheses.??

-H₀: ?₀ = 0
H_a: ?₀ ≠ 0

-H₀: ?₁ = 0
H_a: ?₁ ≠ 0

-H₀: ?₀ ≠ 0
H_a: ?₀ = 0

-H₀: ?₁ ≠ 0
H_a: ?₁ = 0

-H₀: ?₁ ≥ 0
H_a: ?₁ < 0

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

test statistic=??

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

p-value = ??

What is your conclusion?

-Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.

-Reject H₀. We conclude that the relationship between price ($) and overall score is significant.

- Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

-Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b)

Test for a significant relationship using the F test. Use ? = 0.05.

State the null and alternative hypotheses.

-H₀: ?₁ ≠ 0
H_a: ?₁ = 0

-H₀: ?₀ ≠ 0
H_a: ?₀ = 0

- H₀: ?₀ = 0
H_a: ?₀ ≠ 0

-H₀: ?₁ = 0
H_a: ?₁ ≠ 0

-H₀: ?₁ ≥ 0
H_a: ?₁ < 0

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

Test statistic=??

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

p-value = ??

What is your conclusion?

-Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.

-Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

- Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

-Reject H₀. 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 of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Regression	?	?	?	?	?
Error	?	?	?
Total	?	?

Expert Solution

Step 1

applying regression:

null hypothesis:Ho:		β₁	=	0
Alternate Hypothesis: Ha:		β₁	≠	0

test stat t =

β₁/se(β₁)=

4.586

p value =0.010

reject Ho, we conclude.........

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