4) As a measure ofproductivity, a cell phone company records the number of customers each of its retail employees activates weekly. An activation is defined as either a new customer signing a cell phone contract or an existing customer renewing a contract. The accompanying table shows the number of weekly activations for eight randomly selected employees along with theirjob-satisfaction levels rated on a scale of1-10 (10=Most satisfied). Let satisfaction be the independent variable and let activations be the dependent variable. Complete parts a through c.

Satisfaction

33 8.0

27 7.9

41 8.5

36 9.0

18 6.1

29 7.0

32 8.2

22 7.7

a. Using =0.05, test the significance of the regression slope.

The hypotheses for this test are Upper H 0 :

The test statistic is----.

(Type an integer or decimal rounded to two decimal places asneeded.)

Thep-value is----.

(Type an integer or decimal rounded to three decimal places asneeded.)

Therefore, at the 0.05 level ofsignificance, ----- the null hypothesis. There ---- sufficient evidence to conclude that the slope -----different from zero.

b. Construct a 95% confidence interval for the population slope.

The confidence interval is (----,----)

(Type integers or decimals rounded to three decimal places asneeded.)

c. What conclusions about the number of weekly activations and job satisfaction can be drawn from theseresults?

The conclusion is that ------ a linear relationship between satisfaction and activations because the null hypothesis ----- rejected and because the confidence interval for the population slope ----- contain 0.

5) A medicine board would like to investigate the theory that amother's shoe size can be used to predict aninfant's birth weight in pounds. The accompanying table records a random sample of the shoe sizes of 10 mothers and the birth weights of their infants. Complete parts a through f.

ShoeSize BirthWeight

7.5 7.3

8.0 7.9

9.0 7.9

8.5 9.3

8.5 7.5

8.0 6.7

8.5 9.1

7.5 6.5

8.0 9.2

9.0 10.0

b. Calculate the slope andy-intercept for the regression formula.

The slope is --- and they-intercept is -----.

(Type integers or decimals rounded to three decimal places asneeded.)

c. Provide an interpretation for the value of the slope.

The slope indicates an increase of one in shoe size corresponds to an increase of-----

in the average number of birth weight.

(Type an integer or decimal rounded to three decimal places asneeded.)

d. Predict the birth weight of shoe size of 7.0

The predicted number of activations is-----.

(Round to the nearest whole number asneeded.)

e. Calculate the SST.

SST=------

(Type an integer or decimal rounded to two decimal places asneeded.)

f. Partition the SST into the SSR and the SSE.

SSR=----- and SSE=-----

(Type integers or decimals rounded to two decimal places asneeded.)

6)A medicine board would like to investigate the theory that amother's shoe size can be used to predict aninfant's birth weight in pounds. The accompanying table records a random sample of the shoe sizes of 10 mothers and the birth weights of their infants. Complete parts a through c.

ShoeSize

BirthWeight

7.5 7.2

8.0 7.7

9.0 8.1

8.5 9.5

8.5 7.9

8.0 6.7

8.5 9.1

7.5 6.5

8.0 9.2

9.0 9.9

a. Calculate the correlation coefficient for this sample.

The correlation coefficient is-----.

(Type an integer or decimal rounded to three decimal places asneeded.)

b. Using =0.01, test to determine if the population correlation coefficient is greater than zero.

The hypotheses for this test are Upper H 0 : ---------------------------------.

The test statistic is-----.

(Type an integer or decimal rounded to two decimal places asneeded.)

Thep-value is-----.

(Type an integer or decimal rounded to three decimal places asneeded.)

Therefore, at the 0.01 level ofsignificance, fail to------ the null hypothesis. There------ sufficient evidence to conclude that the population correlation coefficient is------ zero.

c. What conclusions can be made based on theseresults?a linear relationship between shoesize and birthweight.