(1) The production department of Celltronics International wants to explore the relationship between
the number of employees who assemble a subassembly and the number produced. As an experiment,
3 employees were assigned to assemble the subassemblies. They produced 8 during a one-hour
period. Then 5 employees assembled them. They produced 13 during a one-hour period. The
complete set of paired observations follows.
Number of
Assemblers
3
5
2
6
4
One-Hour
Production (units)
8
13
5
23
16
The dependent variable is production; that is, it is assumed that different levels of production result from a different
number of employees.
(b) A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number
of assemblers and production?
, as the number of assemblers , so does the production.
(c) Compute the coefficient of correlation. (Negative amount should be indicated by a minus sign. Round sx, sy
and r to 3 decimal places.)
X
Y
3
5
2
(
8
13
5
(
)2
-5
1
)2
(
1
-8
)(
)
25
0
64
6
4
=
sy =
23
16
2
3
=
4
0
sx =
r=
A study of 16 worldwide financial institutions showed the correlation between their assets and pretax profit to be .
77.
(1) State the decision rule for .05 significance level: Ho: ρ 0; H1: ρ > 0 (Round your answer to 3 decimal
places.)
Reject Ho if t>
(2) Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
(3) Can we conclude that the correlation in the population is greater than zero? Use the .05 significance level
Ho . It is to conclude that there is positive association in the
population between assets and pretax profit.
20
0
(2) A study of 16 worldwide financial institutions showed the correlation between their assets and
pretax profit to be .77.
(1) State the decision rule for .05 significance level: Ho: ρ 0; H1: ρ > 0 (Round your answer to 3 decimal
places.)
Reject Ho if t>
(2) Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
(3) Can we conclude that the correlation in the population is greater than zero? Use the .05 significance level
Ho . It is to conclude that there is positive association in the
population between assets and pretax profit.
(3) The following sample observations were randomly selected. (Round your answers to 2 decimal
places.)
X
:
4
5
3
6
10
Y
:
(a)
(b)
10.8
12.6
8
15.4 18.6
The regression equation is Y' = + X
When X is 9.5 this gives Y' =
(4) Given the following ANOVA table:
Source
Regression
Error
Total
DF
1
12
SS
1,250
625
13
MS
1,250.00
52.08
F
24.00
1,875
(a) Determine the coefficient of determination.(Round your answer to 3 decimal places.)
Coefficient of determination
(b) Assuming a direct relationship between the variables, what is the correlation coefficient? (Round your answer
to 2 decimal places.)
Coefficient of correlation
(c) Determine the standard error of estimate. (Round your answer to 2 decimal places.)
Standard error of estimate
(5) Waterbury Insurance Company wants to study the relationship between the amount of fire damage and
the distance between the burning house and the nearest fire station. This information will be used in setting
rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial
department determined the distance from the fire station (X) and the amount of fire damage, in thousands of
dollars (Y). The MegaStat output is reported below.
ANOVA table
Sou
SS df MS
rce
1,8
Reg
64.
ress
578
ion
2
1,3
Res
44.
idua
493
l
4
3,2
Tot
09.
al
071
6
Regression output
Coeff
Varia
Std.
icient
bles
Error
s
Interc
12.36
ept
01
Dista
4.795
nce6
X
F
1
1,8
64.
578
2
28
48.
017
6
38.
83
29
t(df=28)
3.291
5
3.755
0.769
6
6.23
(a-1) Write out the regression equation. (Round your answers to 3 decimal places.)
Y = + X.
(a-2) Is there a direct or indirect relationship between the distance from the fire station and the amount of fire
damage?
The relationship between distance and damage is .
(b) How much damage would you estimate (in dollars) for a fire 5 miles from the nearest fire station? (Round your
answer to the nearest dollar amount. Omit the "$" sign in your response.)
Estimated damage
$
(c-1) Determine the coefficient of determination. (Round your answer to 3 decimal places.)
Coefficient of determination
(c-2) Fill in the blank below. (Round your answer to 1 decimal place. Omit the "%" sign in your response.)
% of the variation in damage is explained by variation in distance.
(d-1) Determine the coefficient of correlation. (Round your answer to 3 decimal places.)
Coefficient of correlation
(d-2) Choose the right option.
There is a fairly solid link between the variables.
(d-3) How did you determine the sign of the correlation coefficient?
It is because the slope is .
(e-1) State the decision rule for .01 significance level: H0 : ρ = 0; H1 : ρ 0. (Negative amounts should be
indicated by a minus sign. Round your answers to 3 decimal places.)
Reject H0 if t < or t >
(e-2) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
(e-3) Is there any significant relationship between the distance from the fire station and the amount of damage? Use
the .01 significance level.
H0. There is relationship between distance and fire damage.
(6) The following sample observations were randomly selected. (Do not round the intermediate values.
Round your answers to 2 decimal places.)
X
:
Y
:
4
5
3
7.7
5
8.9
6
10
15.3 22.5
(a) Determine the 0.95 confidence interval for the mean predicted when
X=6(,)
(b) Determine the 0.95 prediction interval for an individual predicted when
X=6(,)