Question

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows. Brand Price Score Bose 180 78 Scullcandy 160 76 Koss 85 65 Phillips/O'Neill 70 56 Denon 80 40 JVC 45 27 a. Does the t test indicate a significant relationship between price and the overall score? The test t-Conclusion at α = .05 t = (to 2 decimal places.) p-value is What is your conclusion? Use α = .05. . b. Test for a significant relationship using the F test. p-value is What is your conclusion? Use α = .05. Because p-value is .05, we H0: β1 is . c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Regression Error Total

Answer 1

Price	Score
180	78
160	76
85	65
70	56
80	40
45	27

using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8650
R Square	0.7482
Adjusted R Square	0.6852
Standard Error	11.3775
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1538.2094	1538.2094	11.8829	0.0261
Residual	4	517.7906	129.4476
Total	5	2056.0000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	23.3245	10.8171	2.1563	0.0973	-6.7085
Price	0.3259	0.0945	3.4472	0.0261	0.0634

a)

t = 3.45

p-value = 0.0261

p-value < 0.05

hence we reject the null hypothesis

we conclude that there is significant relationship

b)

F = 11.8829

p-value = 0.0261

p-value < 0.05

hence we reject the null hypothesis

we conclude that there is significant relationship

c)

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1538.209	1538.209	11.883	0.026
Residual	4	517.791	129.448
Total	5	2056.000