Question

# You may need to use the appropriate technology to answer this question. Consider the following data...

You may need to use the appropriate technology to answer this question.

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 71
C 95 61
D 70 58
E 70 42
F 35 28

(a)

The estimated regression equation for this data is

ŷ = 25.866 + 0.301x,

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 =

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.    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.

(b)

Test for a significant relationship using the F test. 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: β0 ≠ 0
Ha: β0 = 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 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 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.

(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

a)

 from excel: data-data analysis: regression:

H0: β1 = 0
Ha: β1 ≠ 0

value of the test statistic = 4.432

 P value    = 0.0114 (from excel:tdist(4.4318,4,2)

since p value <0.05:

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 =19.64

 P value    = 0.011 (from excel:tdist(4.4318,4,2)

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

c)

 Source SS df MS F p value regression 1357.53 1 1357.53 19.64 0.011 Residual error 276.47 4 69.12 Total 1634.00 5

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