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 76 150 69 95 63 70 54 70 38 35 24

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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
76
В
150
69
95
63
D
70
54
E
70
38
F
35
24
(a) The estimated regression equation for this data is ŷ = 21.258 + 0.327x, where x =
price ($) and y
= overall score. Does the t test indicate a significant relationship between price and the overall
score? Use a = 0.05.
State the null and alternative hypotheses.
Ho: B1 + 0
Ha: B1
= 0
O Ho: B1 = 0
Hai B1 # 0
Ho: Bo
= 0
H: Bo + 0
Ho: B1 2 0
Ha: B1 < 0
Ho: Bo + 0
Ha: Bo
= 0
Find the value of the test statistic. (Round your answer to three decimal places.)
11.45
Find the p-value. (Round your answer to four decimal places.)
p-value
0.00
Transcribed Image Text:Consider the following data on price ($) 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 ($) Score A 180 76 В 150 69 95 63 D 70 54 E 70 38 F 35 24 (a) The estimated regression equation for this data is ŷ = 21.258 + 0.327x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use a = 0.05. State the null and alternative hypotheses. Ho: B1 + 0 Ha: B1 = 0 O Ho: B1 = 0 Hai B1 # 0 Ho: Bo = 0 H: Bo + 0 Ho: B1 2 0 Ha: B1 < 0 Ho: Bo + 0 Ha: Bo = 0 Find the value of the test statistic. (Round your answer to three decimal places.) 11.45 Find the p-value. (Round your answer to four decimal places.) p-value 0.00
Ho: B, + 0
H3: B1 = 0
O Ho: B1 2 0
Ha: B1 < 0
Ho: Bo + 0
Hgi Bo = 0
O Ho: Bo = 0
Hạ: Bo # 0
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
What is your conclusion?
Do not reject Ho: We conclude that the relationship between price ($) and overall score is significant.
Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant.
Reject Ho. We conclude that the relationship between price ($) and overall score is significant.
Do not reject Ho. We cannot conclude that the relationship between price ($) and overall score is
significant.
(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
Sum
Mean
Degrees
of Freedom
F
p-value
of Variation
of Squares
Square
Regression
5078400
13.11
Error
Total
Transcribed Image Text:Ho: B, + 0 H3: B1 = 0 O Ho: B1 2 0 Ha: B1 < 0 Ho: Bo + 0 Hgi Bo = 0 O Ho: Bo = 0 Hạ: Bo # 0 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 What is your conclusion? Do not reject Ho: We conclude that the relationship between price ($) and overall score is significant. Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. Reject Ho. We conclude that the relationship between price ($) and overall score is significant. Do not reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. (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 Sum Mean Degrees of Freedom F p-value of Variation of Squares Square Regression 5078400 13.11 Error Total
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