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 | 8,600 |

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 − 1,434* x*.

For these data, SSE = 6,833,947.38 and SST = 51,535,800. Use the
*F* test to determine whether the weight for a bike and the
price are related at the 0.05 level of significance.

State the null and alternative hypotheses.

*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

*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 =

State your conclusion.

Reject *H*_{0}. We conclude that the relationship
between weight (pounds) and price ($) is significant.

Reject *H*_{0}. We cannot conclude that the
relationship between weight (pounds) and price ($) is
significant.

Do not reject *H*_{0}. We conclude that the
relationship between weight (pounds) and price ($) is
significant.

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

Answer #1

The statistical software output for this problem is :

*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠ 0

Test statistics = 52.33

P-value = 0.000

Reject *H*_{0}. We conclude that the relationship
between weight (pounds) and price ($) is significant.

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
6,350
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
2,680
I
17.6
3,500
J
14.1
8,000
These data provided the estimated regression
equation ŷ = 28,175 − 1,413x.
For these data, SSE = 7,270,445.08 and SST = 50,662,800. Use the
F test to determine whether...

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...

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...

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
6,150
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
2,680
I
17.6
3,400
J
14.1
8,000
These data provided the estimated regression equation ŷ
= 28,277 − 1,421x.
For these data, SSE = 6,903,351.24 and SST = 50,805,800. 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
6,150
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
2,480
I
17.6
3,300
J
14.1
8,000
These data provided the estimated regression
equation ŷ = 28,750 − 1,452x.
For these data, SSE = 7,198,472.68 and SST = 53,025,800.Use the
F test to determine whether the...

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 + 0.323x,
where x...

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...

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...

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:...

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...

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