Question

In: Statistics and Probability

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 56
E 70 38
F 35 28

(a) The estimated regression equation for this data is  ŷ = 24.799 + 0.302x, 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 ≠ 0

H0: β0 ≠ 0
Ha: β0 = 0

H0: β1 ≠ 0
Ha: β1 = 0

H0: β1 ≥ 0
Ha: β1 < 0

H0: β0 = 0
Ha: β0 ≠ 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 =

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 =  

(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

Solutions

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