Question

# Consider the following data on price (\$) and the overall score for six stereo headphones tested...

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 74
B 150 71
C 95 63
D 70 54
E 70 38
F 35 24

(a)

The estimated regression equation for this data is

ŷ = 21.659 + 0.323x,

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.

H0: β1 = 0
Ha: β1 ≠ 0H0: β1 ≥ 0
Ha: β1 < 0    H0: β0 = 0
Ha: β0 ≠ 0H0: β1 ≠ 0
Ha: β1 = 0H0: β0 ≠ 0
Ha: β0 = 0

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

Do not 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.     Reject H0. We cannot conclude that the relationship between price (\$) and overall score is significant.Do not reject H0. We conclude that the relationship between price (\$) and overall score is significant.

(b)

Test for a significant relationship using the F test. Use α = 0.05.

State the null and alternative hypotheses.

H0: β0 = 0
Ha: β0 ≠ 0H0: β1 ≥ 0
Ha: β1 < 0    H0: β0 ≠ 0
Ha: β0 = 0H0: β1 = 0
Ha: β1 ≠ 0H0: β1 ≠ 0
Ha: β1 = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =

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.     Do not 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.

(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

Applying one way ANOVA from excel: data-data analysis:

H0: β1 = 0
Ha: β1 ≠ 0

value of the test statistic =4.155

 p value: = 0.0142

Reject H0. We conclude that the relationship between price (\$) and overall score is significant.

b)

H0: β1 = 0
Ha: β1 ≠ 0

value of the test statistic =17.26

p value =0.014

Reject H0. We conclude that the relationship between price (\$) and overall score is significant

c)

 Source SS df MS F p value regression 1563.69 1 1563.69 17.26 0.014 Residual error 362.31 4 90.58 Total 1926.00 5

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