Question

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 + 0.301* x*,

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.

*H*_{0}: *β*_{1} ≥ 0

*H*_{a}: *β*_{1} <
0*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠
0 *H*_{0}:
*β*_{0} = 0

*H*_{a}: *β*_{0} ≠
0*H*_{0}: *β*_{1} ≠ 0

*H*_{a}: *β*_{1} =
0*H*_{0}: *β*_{0} ≠ 0

*H*_{a}: *β*_{0} = 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 =

What is your conclusion?

Reject *H*_{0}. We cannot conclude that the
relationship between price ($) and overall score is significant.Do
not reject *H*_{0}. We conclude that the
relationship between price ($) and overall score is
significant. Do not reject
*H*_{0}. We cannot conclude that the relationship
between price ($) and overall score is significant.Reject
*H*_{0}. We conclude that the relationship between
price ($) 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.

*H*_{0}: *β*_{1} ≠ 0

*H*_{a}: *β*_{1} =
0*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠
0 *H*_{0}:
*β*_{0} = 0

*H*_{a}: *β*_{0} ≠
0*H*_{0}: *β*_{0} ≠ 0

*H*_{a}: *β*_{0} =
0*H*_{0}: *β*_{1} ≥ 0

*H*_{a}: *β*_{1} < 0

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 =

What is your conclusion?

Reject *H*_{0}. We cannot conclude that the
relationship between price ($) and overall score is significant.Do
not reject *H*_{0}. We conclude that the
relationship between price ($) and overall score is
significant. Reject *H*_{0}.
We conclude that the relationship between price ($) and overall
score is significant.Do not reject *H*_{0}. We
cannot conclude that the relationship between price ($) 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 |

Answer #1

a)

from excel: data-data analysis: regression: |

*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠ 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 *H*_{0}. We conclude that the relationship
between price ($) and overall score is significant.

b)

*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠ 0

value of the test statistic =19.64

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

Reject *H*_{0}. 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 |

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
69
C
95
63
D
70
56
E
70
38
F
35
28
(a)
The estimated regression...

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(b)Test for a significant relationship by using the t
test. Use α = 0.05.
State the null and alternative hypotheses.
a) H0: β0 = 0
Ha: β0 ≠ 0
b) H0: β1 = 0...

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
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(a)
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9
13
20
yi
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18
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26
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