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	63
D	70	54
E	70	38
F	35	24

(a)

The estimated regression equation for this data is

ŷ = 21.659 + 0.323x,

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

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.     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 one way ANOVA from excel: data-data analysis:

H₀: β₁ = 0
H_a: β₁ ≠ 0

value of the test statistic =4.155

p value:

=

0.0142

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 =17.26

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	1563.69	1	1563.69	17.26	0.014
Residual error	362.31	4	90.58
Total	1926.00	5