Exercises. a) Construct a scatter diagram

1. For the data set

x	0 1 6 3 5
y	4 3 0 2 1

a) Construct a scatter diagram

b) Guess the sign and value of the correlation coefficient

c) Calculate the correlation coefficient.

2. A sample data set produced the following information.

; ; ; ;

; and

Calculate the linear correlation coefficient .

3. Calculations from a data set of pairs of (x, y) values have provided the following results

; ;

Calculate the linear correlation coefficient.

4. The following table gives the experience (in years) and monthly salaries (in hundred of dollars) of nine randomly selected secretaries

Experience	14 3 5 6 4 9 18 5 16 16
Monthly salary	22 12 15 17 15 19 24 13 27

a) Do you expect the experience and monthly salaries to be positive or negatively related?

b) Compute the correlation coefficient.

c) Test at the 10% significance level, against a two sided alternative, the null hypothesis that the population correlation coefficient is zero.

5. The following data were collected regarding the starting monthly salary and the grade point average (GPA) for students who had obtained a degree in business administration and economics:

GPA	2.6 3.4 3.6 3.2 3.5 2.9
Monthly salary ($)	900 1200 600 1100 1400 1000

a) Develop a scatter diagram for the above data.

b) Compute the sample correlation coefficient between grade point average and salary.

c) Test at the 5% significance level the null hypothesis that the population correlation coefficient is zero against the alternative that it is positive.

6. The management of a supermarket wanted to check the effect of the number of broadcast on TV on the gross sales at the store. The management experimented for eight weeks by broadcasting a different number of commercials each week on TV. The following table gives the number of commercials during each week and the gross sales (in 1000’s of dollars)

Number of commercials	22 16 28 12 30 19 24 32
Gross sales per week	3.64 3.12 4.08 2.84 3.98 3.55 4.02 4.38

a) Compute the sample correlation coefficient between number of broadcasts and gross sales.

b) Test the null hypothesis that number of broadcasts and gross sales are uncorrelated in the population against the alternative that population correlation is positive.

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