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	78
B	150	71
C	95	63
D	70	58
E	70	38
F	35	28

(a) The estimated regression equation for this data is ŷ = 24.060 + 0.319x, 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. State the null and alternative hypotheses."

(b) Find the value of the test statistic and the P-Value using Excel Data Analysis. (Round your answer to three decimal places.)

(c) Test for a significant relationship using the F test and find the P-Value using Excel Data Analysis. Use α = 0.05. State the null and alternative hypotheses.

Answer 1

Answer (a)

Null Hypothesis,Ho: There is no significant relationship between price and overall score i.e.

Alternative Hypothesis,Ha: There is significant relationship between price and overall score i.e.

Answer (b)

Test-Statistics: t = 4.206

p-value = 0.014

Answer (c)

F-value = 17.689 and p-value = 0.014

Since, p-value < 0.05 so we Reject the Null Hypothesis and conclude that there is significant difference between price and overall score

Excel Output: