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 186 78 Scullcandy 162 78 Koss 90 60 Phillips/O'Neill 78 54 Denon 72 42 JVC 36 30 a. Does the t test indicate a significant relationship between price and the overall score? The test t-Conclusion at = .05 t = (to 2 decimal places.) p-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 = .05. - Select your answer -There is a significant relationship between price and overall score There is no significant relationship between price and overall score Item 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 = .05. Because p-value is - Select your answer -greater than or equal to less than or equal to equal to Item 5 .05, we - Select your answer -accept reject Item 6 H 0: β 1 is - Select your answer -greater than or equal to zero less than or equal to zero equal to zero Item 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

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
186	78	6724.00	441.00	1722.00
162	78	3364.00	441.00	1218.00
90	60	196.00	9.00	-42.00
78	54	676.00	9.00	78.00
72	42	1024.00	225.00	480.00
36	30	4624.00	729.00	1836.00

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	624	342	16608	1854.000	5292.000
mean	104.000	57.000	SSxx	SSyy	SSxy

sample size ,   n =   6          
here, x̅ = Σx / n=   104.00   ,     ȳ = Σy/n =   57.00  
                  
SSxx =    Σ(x-x̅)² =    16608.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   5292.0          
                  
estimated slope , ß1 = SSxy/SSxx =   5292.0   /   16608.000   =   0.31864
                  
intercept,   ß0 = y̅-ß1* x̄ =   23.86127          
                  
so, regression line is   Ŷ =   23.86   +   0.3186   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    167.7486          
                  
std error ,Se =    √(SSE/(n-2)) =    6.4759          
---------------

a)

Ho:   ß1=   0          
H1:   ß1╪   0          
n=   6              
alpha =   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    6.476   /√   16608.00   =   0.0503
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    0.3186   /   0.0503   =   6.34

p-value is-less than .01

There is a significant relationship between price and overall score

b)

p-value is-less than .01

we -reject H ₀: β ₁ is greater than or equal to zero

c)

Anova table
variation	SS	df	MS	F-stat	p-value
regression	1686.251	1	1686.251	40.209	less than 0.01
error,	167.749	4	41.937
total	1854.000	5