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To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the

=0.01

level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

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Height of

Father, Xi

Height of Son, Yi

71.5

76.6

72.7

76.2

68.6

71.1

70.3

72.2

66.6

67.7

72.1

72.6

67.9

67.8

69.2

68.7

71.7

70.4

71.5

69.6

73.2

70.8

68.5

65.0

69.2

64.3

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Which conditions must be met by the sample for this test? Select all that apply.

A.

The sampling method results in an independent sample.

B.

The sample size must be large.

C.

The sample size is no more than 5% of the population size.

D.

The differences are normally distributed or the sample size is large.

E.

The sampling method results in a dependent sample.

Let

di=XiYi.

Write the hypotheses for the test.

H0:

mu Subscript d Baseline not equals 0d0

mu Subscript d Baseline equals 0d=0

mu Subscript d Baseline greater than 0d>0

mu Subscript d Baseline less than 0d<0

H1:

mu Subscript d Baseline equals 0d=0

mu Subscript d Baseline less than 0d<0

mu Subscript d Baseline not equals 0d0

mu Subscript d Baseline greater than 0d>0

Calculate the test statistic.

t0=nothing

(Round to two decimal places as needed.)

Calculate the P-value.

P-value=nothing

(Round to three decimal places as needed.)

Should the null hypothesis be rejected?

Reject

Do not reject

H0

because the P-value is

greater than

less than

the level of significance. There

is

is not

sufficient evidence to conclude that sons

are taller than

are the same height as

are shorter than

are not the same height as

their fathers at the

0.01

level of significance.

Is the type of area that a person lives in a factor in the age that a person experiences their first passionate kiss? The table below shows data that was collected.

Rural

Suburbs

City

19

17

19

14

14

14

13

14

17

16

14

15

15

13

16

17

14

16

19

19

12

12

14

16

13

18

Assume that all distributions are normal, the three population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of =0.1=0.1.

The test-statistic for this data: F =

The p-value for this sample =

A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information.

x (number of job changes)

5

3

6

6

1

5

9

10

10

3

y (Salary in $1000)

36

37

34

32

32

38

43

37

40

33

x = 58; y = 362; x2 = 422; y2 = 13,220; xy = 2,165

(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.)

x

=

y

=

b

=

=

+ x

(b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.

(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

r =

r2 =

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

%