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 (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:
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