Question

Consider the data set below.

xx | 55 | 22 | 66 | 33 | 22 | 77 |

yy | 99 | 22 | 99 | 88 | 33 | 66 |

For a hypothesis test, where H0:β1=0H0:β1=0 and H1:β1≠0H1:β1≠0, and
using α=0.01α=0.01, give the following:

(a) The test statistic

t=t=

(b) The degree of freedom

df=df=

(c) The rejection region

|t|>|t|>

The final conclustion is

**A.** There is not sufficient evidence to reject the
null hypothesis that β1=0β1=0.

**B.** We can reject the null hypothesis that β1=0β1=0
and accept that β1≠0β1≠0.

Answer #1

The statistic software output for this problem is :

Simple linear regression results:

Dependent Variable: y

Independent Variable: x

y = 2.3649635 + 0.91240876 x

Sample size: 6

R (correlation coefficient) = 0.63708381

R-sq = 0.40587578

Estimate of error standard deviation: 2.6374617

Parameter estimates:

Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|

Intercept | 2.3649635 | 2.5393803 | ≠ 0 | 4 | 0.93131522 | 0.4044 |

Slope | 0.91240876 | 0.55195225 | ≠ 0 | 4 | 1.6530574 | 0.1737 |

(a) The test statistic

t = 1.653

(b) The degree of freedom

df = 4

(c) The rejection region

|t| > 4.604

(d)

**A.** There is not sufficient evidence to reject
the null hypothesis that β1=0

(1 point) Consider the data set below
x
y
8
9
7
2
7
2
9
8
4
8
3
8
For a hypothesis test, where ?0:?1=0H0:β1=0 and ?1:?1≠0H1:β1≠0,
and using ?=0.05α=0.05, give the following:
(a) The test statistic
?=
(b) The degree of freedom
??=
(c) The rejection region
|?|>
The final conclustion is
A. There is not sufficient evidence to reject
the null hypothesis that ?1=0β1=0.
B. We can reject the null hypothesis that ?1=0β1=0
and accept that ?1≠0β1≠0.

Consider the following two sample data sets.
Set 1:
99
22
77
55
88
Set 2:
66
1313
1818
77
22
a. Calculate the coefficient of variation for each data set.
b. Which data set has more variability?
a. The coefficient of variation for set 1 is
nothing%.
(Round to one decimal place as needed.)
The coefficient of variation for set 2 is
nothing%.
(Round to one decimal place as needed.)
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x
4
6
3
8
7
6
y
1
3
9
1
8
6
For a hyopthesis test, where H0:?1=0 and H1:?1?0, and using
?=0.01, give the following:
(a) The test statistic t=
(b) The degree of freedom df=
(c) The rejection region |t|>

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Consider the following regression model
Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + β5X5i + ui
This model has been estimated by OLS. The Gretl output is
below.
Model 1: OLS, using observations 1-52
coefficient
std. error
t-ratio
p-value
const
-0.5186
0.8624
-0.6013
0.5506
X1
0.1497
0.4125
0.3630
0.7182
X2
-0.2710
0.1714
-1.5808
0.1208
X3
0.1809
0.6028
0.3001
0.7654
X4
0.4574
0.2729
1.6757
0.1006
X5
2.4438
0.1781
13.7200
0.0000
Mean dependent var
1.3617
S.D. dependent...

A sample of scores for men and women from an examination in
Statistics 201 were:
Men
88
70
87
53
45
58
71
48
61
81
Women
70
77
60
84
74
89
94
50
66
61
Given that the null hypothesis and the alternative hypothesis
are:
H0: μm -
μw ≤ -2
H1: μm - μw
> -2
and using a 0.05 significance level conduct a t-test
about a difference in population means:
a)
What is the correct decision...

The management for a large grocery store chain would like to
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measured for both the old cash register and the new cash
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Without making any assumptions about the distribution, do the data
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Problem 1. Consider the GASTURBINE data set and corresponding
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The first 10 observations are given for illustrative purposes.
Complete parts a) through g) below.
ENGINE
SHAFTS
RPM
CPRATIO
INLET-TEMP
EXH-TEMP
AIRFLOW
POWER
HEATRATE
Traditional
1
27245
9.2
1134
602
7
1630
14622
Traditional
1
14000
12.2
950
446
15
2726
13196
Traditional
1
17384
14.8
1149
537
20
5247
11948
Traditional
1...

StudentNO
Gender
Height in inchese
1
Female
63
2
Female
64.0
3
Male
67.0
4
Female
59
5
Male
60
6
Female
61
7
Female
62
8
Female
63
9
Female
63
10
Female
64
11
Male
64
12
Female
65
13
Female
65
14
Female
65
15
Female
65
16
Female
66
17
Female
66
18
Male
67
19
Male
67
20
Male
67
21
Female
67
22
Male
67
23
Male
67
24
Female
67.5
25
Male
68...

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Sales
LastRate
Location
398
290
8
Suburban
45
243
9
Urban
25
289
6.5
Urban
378
207
4.5
Rural
64
275
6
Rural
373
275
5.5
Urban
41
209
6
Urban
84
265
9
Urban
27
290
8
Suburban
36
319
7
Urban
99
327
7.5
Suburban
68
154
6.5
Suburban
18
356
5.5
Urban
29
321
6.5
Urban
28
307
7.5
Suburban
45
213
6.5
Suburban
122
273
5.5
Suburban
51
239
4.5
Suburban
24
259
6
Rural...

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