Question

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	Price ($)	Score
A	180	74
B	150	71
C	95	59
D	70	56
E	70	40
F	35	24

(a)

The estimated regression equation for this data is

ŷ = 22.328 + 0.317x,

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.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ ≥ 0
H_a: β₁ < 0    H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₁ ≠ 0
H_a: β₁ = 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?

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.     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.

(b)

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

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ ≠ 0
H_a: β₁ = 0    H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₀ = 0
H_a: β₀ ≠ 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?

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

(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

Answer 1

SSE =Syy-(Sxy)2/Sxx=

314.3194

	s2 =SSE/(n-2)=	78.5798
std error σ              =	=se =√s2=	8.8645

estimated std error of slope =se(β1) =s/√Sxx=

0.0725

a)

H₀: β₀ = 0
H_a: β₀ ≠ 0

test stat t =	(bo-β1)/se(β1)=	=	4.369
p value:		=	0.0120

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

b)

H₀: β₁ = 0
H_a: β₁ ≠ 0

value of the test statistic =19.08

p value =0.012

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

c)

Source	SS	df	MS	F	p value
regression	1499.68	1	1499.68	19.08	0.012
Residual error	314.32	4	78.58
Total	1814.00	5