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 73 C 95 63 D 70 58 E 70 40 F 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 78
B 150 73
C 95 63
D 70 58
E 70 40
F 35 24
(a) The estimated regression equation for this data is 
ŷ = 22.054 + 0.339x,
 where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use ? = 0.05.
State the null and alternative hypotheses.??
-H0: ?0 = 0
Ha: ?0 ≠ 0
-H0: ?1 = 0
Ha: ?1 ≠ 0    
-H0: ?0 ≠ 0
Ha: ?0 = 0
-H0: ?1 ≠ 0
Ha: ?1 = 0
-H0: ?1 ≥ 0
Ha: ?1 < 0
Find the value of the test statistic. (Round your answer to three decimal places.)
test statistic=??
Find the p-value. (Round your answer to four decimal places.)
p-value = ??
What is your conclusion?
-Do not reject H0. We conclude that the relationship between price ($) and overall score is significant.
-Reject H0. We conclude that the relationship between price ($) and overall score is significant.    
- Reject H0. We cannot conclude that the relationship between price ($) and overall score is significant.
-Do not reject H0. We cannot conclude that the relationship between price ($) and overall score is significant.
(b)
Test for a significant relationship using the F test. Use ? = 0.05.
State the null and alternative hypotheses.
-H0: ?1 ≠ 0
Ha: ?1 = 0
-H0: ?0 ≠ 0
Ha: ?0 = 0   
- H0: ?0 = 0
Ha: ?0 ≠ 0
-H0: ?1 = 0
Ha: ?1 ≠ 0
-H0: ?1 ≥ 0
Ha: ?1 < 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Test statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
What is your conclusion?
-Do not reject H0. We conclude that the relationship between price ($) and overall score is significant.
-Do not reject H0. We cannot conclude that the relationship between price ($) and overall score is significant.    
- Reject H0. We cannot conclude that the relationship between price ($) and overall score is significant.
-Reject H0. We 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
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F p-value
Regression ? ? ? ? ?
Error ? ? ?    
Total ? ?      
Expert Solution
Step 1

applying regression:

a)

null hypothesis:Ho: β1 = 0
Alternate Hypothesis: Ha: β1 0

 

test stat t = β1/se(β1)= = 4.586

 p value =0.010

reject Ho, we conclude.........

 

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