You may need to use the appropriate technology to answer this question. Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). Brand A B C D E F | O Ho: Bo= 0 Ha: Bo #0 ⒸH₁: B₁ = 0 Ha: B₁ * 0 O Ho: B₁ ≥ 0 H₂: B₁ <0 Price ($) Ho: B₁ * 0 H₂: B₁ = 0 180 150 95 70 70 35 Score 74 69 59 56 (a) The estimated regression equation for this data is ý = 23.397993 +0.306020x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05. State the null and alternative hypotheses. ọ Ho: Bo # 0 Ha: Bo = 0 42 24 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? O Reject Ho. We cannot conclude that the relationship between price ($) 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. Reject Ho. We conclude that the relationship between price ($) and overall score is significant.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 22PFA

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Question

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(b) Test for a significant relationship using the F test. Use α = 0.05.
State the null and alternative hypotheses.
H₁: B₁ = 0
Ha: Bo
O Ho: B₁ * 0
Ha: B₁ = 0
# 0
Ho: B₁ = 0
Ha: B₁ * 0
O Ho: B₁ ≥ 0
Ha: B₁ <0
ọ Ho: Bo #0
Ha: Po=
Find the value of the test statistic. (Round your answer to two decimal places.)
= 0
Find the p-value. (Round your answer to three decimal places.)
p-value =
What is your conclusion?
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 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.
(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
Error
Regression
Total
Sum
Degrees
of Squares of Freedom
Mean
Square
F
p-value

Transcribed Image Text:You may need to use the appropriate technology to answer this question. Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). Brand A B C D E F = 0 Ho: Bo = Ha: Bo # 0 Ho: B₁ = 0 Ha: B₁ * 0 Ho: B₁ ≥ 0 Ha: B₁ <0 Price ($) # 0 OHO: B₁ # Ha: B₁ = 0 180 150 95 70 70 35 Score 74 69 59 (a) The estimated regression equation for this data is ŷ = 23.397993 +0.306020x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05. State the null and alternative hypotheses. ọ Ho: Bo #0 Ha: Bo = 0 56 42 24 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? O Reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. Do not reject Ho. We conclude that the relationship between price ($) and overall score significant. Do not reject Ho. We cannot conclude that the relationship between price ($) and overall score is significant. Ⓒ Reject Ho. We conclude that the relationship between price ($) and overall score is significant.

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