Question

You may need to use the appropriate technology to answer this question.

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

Brand	Price ($)	Score
A	180	74
B	150	73
C	95	63
D	70	58
E	70	40
F	35	28

(a)

The estimated regression equation for this data is

ŷ = 25.933 + 0.301x,

where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

(b)

Test for a significant relationship using the F test. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =  

(c)

Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Regression
Error
Total

Answer 1

The statistical software output for this problem is :

(a)

Test statistics = 3.905

P-value = 0.0175

(b)

Test statistics = 15.25

P-value = 0.018

(c)

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	1351.51	1351.51	15.25	0.018
Error	4	354.49	88.62
Total	5	1706