Question

SHOW STEPS IN EXCEL PLEASE

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	40
F	35	24

(a)

The estimated regression equation for this data is

ŷ = 22.726 + 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: β₀ = 0
H_a: β₀ ≠ 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 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.     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 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: 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 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.

(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)

H₀: β₁ = 0
H_a: β₁ ≠ 0

test stat t =	β1/se(β1)=	=	4.099
p value:		=	0.0149

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 =16.80

p-value = 0.015

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

c)

Source	SS	df	MS	F	p value
regression	1557.23	1	1557.23	16.80	0.015
Residual error	370.77	4	92.69
Total	1928.00	5