# MATHEMATICS

2.

The following sample observations were randomly selected.

X             5              3              6              3              4              4              6              8

Y              13           15           7              12           13           11           9              5

Determine the correlation coefficient and interpret the relationship between X and Y.

4.

The production department of Celltronics International wants to explore the relationshipbetween the number of employees who assemble a subassembly and the number produced.

As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced25 during a one-hour period. The complete set of paired observations follows.

One-Hour

Number of          Production

Assemblers        (units)

2              15

4              25

1              10

5              40

3              30

The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.

a. Draw a scatter diagram.

b. Based on the scatter diagram, does there appear to be any relationship between thenumber of assemblers and production? Explain.

c. Compute the correlation coefficient.

6.

The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between theage of a car and its selling price. Listed below is a random sample of 12 used cars soldat the dealership during the last year.

Car Age (years) Selling Price (\$000)          Car Age (years) Selling Price (\$000)

1              9              8.1          7              8              7.6

2              7              6.0          8              11           8.0

3              11           3.6          9              10           8.0

4              12           4.0          10           12           6.0

5              8              5.0          11           6              8.6

6              7              10.0        12           6              8.0

a. Draw a scatter diagram.

b. Determine the correlation coefficient.

c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficientis negative?

8.

The following hypotheses are given.

H0: row >=0

H1: row<0

A random sample of 15 paired observations have a correlation of -.46. Can we concludethat the correlation in the population is less than zero? Use the .05 significance level.

10.

A study of 20 worldwide financial institutions showed the correlation between their assetsand pretax profit to be .86. At the .05 significance level, can we conclude that there ispositive correlation in the population?

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