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 | 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 + 0.323* 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?

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. 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.

(b)

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

State the null and alternative hypotheses.

*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*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠
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 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. Do not reject
*H*_{0}. We conclude that the relationship between
price ($) and overall score is significant.Reject
*H*_{0}. We cannot conclude that the relationship
between price ($) 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

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

*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠ 0

value of the test statistic =4.155

p value: | = | 0.0142 |

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 =17.26

p value =0.014

Reject *H*_{0}. 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 |

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...

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...

Consider the data.
xi
2
6
9
13
20
yi
7
18
10
26
25
(a)
What is the value of the standard error of the estimate? (Round
your answer to three decimal places.)
(b)
Test for a significant relationship by using the t
test. Use α = 0.05.
State the null and alternative hypotheses.
H0: β0 = 0
Ha: β0 ≠
0H0: β1 ≥ 0
Ha: β1 <
0 H0:
β1 ≠ 0
Ha: β1 =
0H0: β0 ≠ 0...

Consider the data.
xi
2
6
9
13
20
yi
5
16
8
24
23
(a)
What is the value of the standard error of the estimate? (Round
your answer to three decimal places.)
(b)
Test for a significant relationship by using the t
test. Use α = 0.05.
State the null and alternative hypotheses.
H0: β0 ≠ 0
Ha: β0 = 0
H0: β1 ≠ 0
Ha: β1 =
0
H0: β1 = 0
Ha: β1 ≠ 0
H0:...

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
58
E
70
40
F
35
24
(a) The estimated regression equation for this data is
ŷ = 23.462 + 0.315x, where
x =...

Consider the following data on x = weight (pounds) and
y = price ($) for 10 road-racing bikes.
Brand
Weight
Price ($)
A
17.8
2,100
B
16.1
6,250
C
14.9
8,370
D
15.9
6,200
E
17.2
4,000
F
13.1
8,600
G
16.2
6,000
H
17.1
2,680
I
17.6
3,400
J
14.1
8,000
These data provided the estimated regression equation
ŷ = 28,503 − 1,434x.
For these data, SSE = 6,833,947.38 and SST = 51,535,800. Use the
F test to determine...

Consider the following data on x = weight (pounds) and
y = price ($) for 10 road-racing bikes.
Brand
Weight
Price ($)
A
17.8
2,100
B
16.1
6,250
C
14.9
8,370
D
15.9
6,200
E
17.2
4,000
F
13.1
8,600
G
16.2
6,000
H
17.1
2,580
I
17.6
3,400
J
14.1
8,000
These data provided the estimated regression equation
ŷ = 28,574 − 1,439x.
For these data, SSE = 7,102,922.54 and SST = 52,120,800. Use the
F test to determine...

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
78
B
150
71
C
95
63
D
70
58
E
70
38
F
35
28
(a) The estimated regression equation for this data is ŷ =
24.060 + 0.319x, where x...

You may need to use the appropriate technology to answer this
question.
Consider the following data on x = weight (pounds) and
y = price ($) for 10 road-racing bikes.
Brand
Weight
Price ($)
A
17.8
2,100
B
16.1
6,250
C
14.9
8,370
D
15.9
6,200
E
17.2
4,000
F
13.1
8,500
G
16.2
6,000
H
17.1
2,580
I
17.6
3,300
J
14.1
8,000
These data provided the estimated regression equation
ŷ = 28,458 − 1,433x.
For these data, SSE...

You may need to use the appropriate technology to answer this
question.
Consider the data.
xi
2
6
9
13
20
yi
7
19
10
28
21
(a) What is the value of the standard error of the estimate?
B)Test for a significant relationship by using the t
test. 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:...

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