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	77
Koss	85	63
Phillips/O'Neill	70	57
Denon	80	40
JVC	35	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 - 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

Solution:

In excel install analysis tool pak and then go to

Data>Data analysis>Regression

Y as Score

X as Price

You will get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.891021
R Square	0.793919
Adjusted R Square	0.742399
Standard Error	10.31701
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1640.237	1640.237	15.40987	0.017167
Residual	4	425.7627	106.4407
Total	5	2066
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	24.17373	9.363065	2.581818	0.06121	-1.82231	50.16976
Price	0.322881	0.082251	3.925541	0.017167	0.094515	0.551248

Intrepretation:

t=3.93

p=0.017167

less than .02

since p<0.05

There is a significant relationship between price and overall score

F stat=15.41

p=0.017167

between .01 and .02

Because p-value is  less than or equal to 0.05

Reject Ho.

ANOVA table

ANOVA
sourceof variation		Sum of squares	Degrees of freedom	Mean square	F	P -vlaue
Regression		1640.237	1	1640.237	15.410	0.017167
Error		425.763	4	106.441
Total		2066.000	5