nsider following data on price ($) and the overall Score SIx stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (hig Brand Price ($) Score A 180 76 B 150 69 95 59 70 58 70 42 F 35 26 a) The estimated regression equation for this data is ý = 24.599 + 0.304x, where x = price ($) and y = overall score. Does thet test indicate a significant relationship between price and the overall score? Use a = 0.05. State the null and alternative hypotheses. O Hạ: Bị = 0 Hoi Bq = 0 O Ho: Bo +0 Hgi Bo = 0 O Ho: Bo = 0 O Ho: Bq = 0 O Hạ: B, 2 0 Hoi Bq

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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
B
150
69
95
59
70
58
E
70
42
35
26
(a) The estimated regression equation for this data is ý = 24.599 + 0.304x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B, + 0
H: B, = 0
O Hoi Bo#0
H3: Bo = 0
O Ho: Bo = 0
H,: Bo = 0
O Ho: B1 = 0
H3: Bq 0
O Hoi Bqz 0
H: B, < 0
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
What is your conclusion?
O Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant.
O Do not reject Ho: We conclude that the relationship between price ($) and overall score is significant.
O Do not reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant.
O Reject Ho. We conclude that the relationship between price ($) and overall score is significant.
Transcribed Image Text:Consider the following data on price ($) 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 ($) Score A 180 76 B 150 69 95 59 70 58 E 70 42 35 26 (a) The estimated regression equation for this data is ý = 24.599 + 0.304x, where x = price ($) 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. O Ho: B, + 0 H: B, = 0 O Hoi Bo#0 H3: Bo = 0 O Ho: Bo = 0 H,: Bo = 0 O Ho: B1 = 0 H3: Bq 0 O Hoi Bqz 0 H: B, < 0 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 = What is your conclusion? O Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. O Do not reject Ho: We conclude that the relationship between price ($) and overall score is significant. O Do not reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. O Reject Ho. We conclude that the relationship between price ($) and overall score is significant.
(b) Test for a significant relationship using the F test. Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B12 0
1
O Ho: B, = 0
H: B, = 0
1
O Ho: B1
1 = 0
Ha: B, = 0
1
O Hoi Bo#0
H: Bo = 0
O Ho: Bo = 0
H: 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?
O Reject Ho. We conclude that the relationship between price ($) and overall score is significant.
Do not reject Ho. We conclude that the relationship between price ($) and overall score is significant.
Reject H,. We cannot 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
Degrees
of Freedom
Mean
F
p-value
of Variation
of Squares
Square
Regression
Error
Total
Transcribed Image Text:(b) Test for a significant relationship using the F test. Use a = 0.05. State the null and alternative hypotheses. O Ho: B12 0 1 O Ho: B, = 0 H: B, = 0 1 O Ho: B1 1 = 0 Ha: B, = 0 1 O Hoi Bo#0 H: Bo = 0 O Ho: Bo = 0 H: 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? O Reject Ho. We conclude that the relationship between price ($) and overall score is significant. Do not reject Ho. We conclude that the relationship between price ($) and overall score is significant. Reject H,. We cannot 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 Degrees of Freedom Mean F p-value of Variation of Squares Square Regression Error Total
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