(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 One-Hour

Production (units)

3 8

5 13

2 5

6 23

4 16

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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 ( )2 ( )2 ( )( )

3 8

-5

25

5 13 1

1

0

2 5

-8

64

6 23 2

4

20

4 16

3 0

0

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=

=

sx =

sy =

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.

(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: 10.8 12.6 8 15.4 18.6

(a) The regression equation is Y' = + X

(b) When X is 9.5 this gives Y' =

(4) Given the following ANOVA table:

Source DF SS MS F

Regression 1 1,250 1,250.00 24.00

Error 12 625 52.08

________________________________________ ________________________________________

Total 13 1,875

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(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

Source SS df MS F

Regression 1,864.5782 1 1,864.5782 38.83

Residual 1,344.4934 28 48.0176

Total 3,209.0716 29

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Regression output

Variables Coefficients Std. Error t(df=28)

Intercept 12.3601 3.2915 3.755

Distance-X 4.7956 0.7696 6.23

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(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: 4 5 3 6 10

Y: 7.7 5 8.9 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 ( , )

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