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	76
B	150	69
C	95	63
D	70	56
E	70	38
F	35	28

(a)

The estimated regression equation for this data is

ŷ = 24.398 + 0.306x,

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: β₀ ≠ 0
H_a: β₀ = 0     H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₀ = 0
H_a: β₀ ≠ 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 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 ($) and overall score is significant. Do not reject H₀. We conclude that the relationship between price ($) 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.

H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₁ ≠ 0
H_a: β₁ = 0     H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₁ ≥ 0
H_a: β₁ < 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 ($) and overall score is significant. Reject H₀. We conclude that the relationship between price ($) and overall score is significant.      Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.Reject H₀. We cannot conclude that the relationship between price ($) 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

Applying regression from excel: data-data analysis: regression:

a)

H₀: β₁ = 0
H_a: β₁ ≠ 0

test stat t =	(bo-β1)/se(β1)=	=	4.184
p value:		=	0.0139

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

b)

H₀: β₀ = 0
H_a: β₀ ≠ 0

value of the test statistic =17.50

p value=0.014

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

c)

Source	SS	df	MS	F	p value
regression	1400.04	1	1400.04	17.50	0.014
Residual error	319.96	4	79.99
Total	1720.00	5