Question

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows. The estimated regression equation for these data is ^y=25.164+0.306x.

Brand	Price	Score
Bose	180	78
Scullcandy	160	71
Koss	85	69
Phillips/O'Neill	80	56
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 a=.05

  (to 2 decimal places.)

-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 2

What is your conclusion? Use a=.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.
-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 a=.05.

Because p-value is - Select your answer - .05 , we - Select your answer- H0: b1 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

	s2 =SSE/(n-2)=	136.1741
std error σ              =	=se =√s2=	11.6694

estimated std error of slope =se(β1) =s/√Sxx=

0.0947

a)

test stat t =

(bo-β1)/se(β1)=

=

3.24

p value is between .025 and .05

There is a significant relationship between price and overall score
b)

test statistic F =10.47

p value is between .025 and .05

Because p-value is less than 0.05 we reject Ho  b1 is zero

c)

Source	SS	df	MS	F	p value
regression	1426.137	1	1426.137	10.473	0.032
Residual error	544.696	4	136.174
Total	1970.833	5