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	71
C	95	61
D	70	58
E	70	42
F	35	28

(a)

The estimated regression equation for this data is

ŷ = 25.866 + 0.301x,

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?

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.    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.

(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: 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 two decimal places.)

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

p-value =

What is your conclusion?

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

a)

from excel: data-data analysis: regression:

H₀: β₁ = 0
H_a: β₁ ≠ 0

value of the test statistic = 4.432

P value    =

0.0114

(from excel:tdist(4.4318,4,2)

since p value <0.05:

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 =19.64

P value    =

0.011

(from excel:tdist(4.4318,4,2)

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

c)

Source	SS	df	MS	F	p value
regression	1357.53	1	1357.53	19.64	0.011
Residual error	276.47	4	69.12
Total	1634.00	5