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	59
D	70	56
E	70	40
F	35	24

(a)

The estimated regression equation for this data is

ŷ = 21.926 + 0.321x,

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

(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?

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

Using Excel<data<megastst<correlation/regression<regression

Here is the output:

Regression Analysis
	r²	0.839
	r	0.916
	Std. Error	8.603
	n	6
	k	1
	Dep. Var.	Score
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,537.9281	1	1,537.9281	20.78	.0104
Residual	296.0719	4	74.0180
Total	1,834.0000	5
Regression output					confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	21.9264	7.86	2.79	0.05	0.09	43.76
Price ($)	0.3207	0.0704	4.558	.0104	0.1254	0.5161

a)

null hypothesis:Ho:		β1	=	0
Alternate Hypothesis: Ha:		β1	≠	0

Test Staistic= 4.558

P value= 0.0104

Since p value <alpha ( Reject null hypothesis)

Conclusion

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

b)

null hypothesis:		β1	=	0
Alternate Hypothesis:		β1	≠	0

test statistic F =20.78

p value =0.0104

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

c)

ANOVA table
Source	Sum of squares SS	df	MS	F	p-value
Regression	1,537.9281	1	1,537.9281	20.78	.0104
Residual	296.0719	4	74.0180
Total	1,834.0000	5

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