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	76
Scullcandy	160	77
Koss	95	63
Phillips/O'Neill	70	56
Denon	80	50
JVC	35	26

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 - Select your answer -less than .02between .02 and .05between .05 and .1between .1 and .2greater than .2Item 2

What is your conclusion? Use α = .05.
- Select your answer -There is a significant relationship between price and overall scoreThere is no significant relationship between price and overall scoreItem 3 .

b. Test for a significant relationship using the F test.
p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 4

What is your conclusion? Use α = .05.

Because p-value is - Select your answer -greater than or equal toless than or equal toequal toItem 5  .05, we - Select your answer -acceptrejectItem 6  H₀: β₁ is - Select your answer -greater than or equal to zeroless than or equal to zeroequal to zeroItem 7 .

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					- Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 12
Error
Total

Answer 1

Applying regression on above data:

	df	SS	MS	F	Significance F
Regression	1	1522.3482	1522.3482	21.7749	0.0095
Residual	4	279.6518	69.9129
Total	5	1802.0000
	Coefficients	Standard Error	t Stat	P-value
Intercept	25.5985	7.7373	3.3084	0.0297
Price	0.3136	0.0672	4.6664	0.0095

a)

test statistic t =4.67

p-value is -less than 0.02

-There is a significant relationship between price and overall score

b)

p-value is   less than .01

Because p-value is less than or equal to 0.05 , reject Ho, β₁ is equal to zero

7)

c)

	SS	df	MS	F	Significance F
Regression	1522.348	1	1522.348	21.775	less than 0.01
Residual	279.652	4	69.913
Total	1802.000	5