7) 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 d.

ShoeSize

BirthWeight

7.5 7.1

8.0 7.8

9.0 8.1

8.5 9.2

8.5 7.7

8.0 6.9

8.5 9.0

7.5 6.6

8.0 9.0

9.0 10.0

a. Calculate the coefficient of determination.

The coefficient of determination is-----.

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

b. Using =0.01, test the significance of the population coefficient of determination.

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, -----------the null hypothesis. There ----- sufficient evidence to conclude that the coefficient of determination is --------- than 0.

c. Construct a 95% confidence interval for the average birth weight for a maternal shoe size of 8.5.

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

(Type integers or decimals rounded to one decimal place asneeded.)

d. Construct a 95% prediction interval for the birth weight for a maternal shoe size of 8.5.

The prediction interval is (----,-----)

(Type integers or decimals rounded to one decimal place asneeded.)

8) 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 7.1

8.0 7.7

9.0 7.8

8.5 9.3

8.5 7.6

8.0 6.8

8.5 9.0

7.5 6.4

8.09.2

9.0 9.8

a. Using =0.01 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 0.10 level ofsignificance, -------- the null hypothesis. There ---- sufficient evidence to conclude that the slope --- different from zero.

b. Construct a 90% 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 maternal shoe size and birth weight can be drawn from theseresults? The conclusion is that there -----

a linear relationship between shoesize and birthweight because the null hypothesis ---- rejected and because the confidence interval for the population slope ----- contains 0.

9) Suppose a teacher recorded the attendance of her students in a recent statistics class because she wanted to investigate the linear relationship between the number of classes they missed and their final grades. The accompanying table shows these data for a random sample of nine students. Complete parts a through f.

MissedClasses

FinalGrade

4 75

6 77

1 95

4 71

0 98

2 86

0 91

5 84

2 97

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 missed classes corresponds to an increase of-----

in the average of final grades

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

d. Predict the number of missed classes for an employee with final grades level of 7.2.

The predicted number of missed classes 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.)