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Is there a significant correlation...

Is there a significant correlation between household income and the size which a child will draw a nickel? Household incomes (in thousands of $) are shown for each of the 75 samples below, along with the size of a nickel drawn by the child:Income (thousands of $) Coin size (mm)

34 30

31 22

24 14

25 18

31 25

18 26

18 31

9 3

38 34

24 23

18 16

31 17

16 23

35 24

8 21

25 32

18 20

8 17

17 16

30 19

13 18

31 16

14 20

14 24

15 21

14 25

21 17

23 18

18 16

28 28

29 21

24 25

28 24

16 15

14 19

18 20

25 21

11 20

10 28

23 16

63 21

56 15

70 21

41 19

98 26

48 27

57 22

75 18

46 23

42 16

67 20

68 19

74 18

54 19

64 18

63 12

64 22

70 24

47 18

81 20

64 18

67 20

52 13

93 14

97 24

92 15

45 11

58 17

74 19

46 17

99 25

90 24

91 14

89 11

88 21You can copy the data into StatCrunch by highlighting the data, right-clicking and selecting Copy (or Ctrl + c), then open the StatCrunch window, click on the first cell, and right-clicking and selecting Paste (or Ctrl + v).Test the claim that there is significant correlation at the 0.01 significance level using a linear regression t-test for the slope. Retain at least 3 decimals on all values.a) Identify the correct hypotheses.

H

0

:

r

=

0

H

A

:

r

≠

0

H

0

:

p

L

o

w

=

p

H

i

g

h

H

A

:

p

L

o

w

≠

p

H

i

g

h

H

0

:

μ

=

0

H

A

:

μ

≠

0

H

0

:

β

=

0

H

A

:

β

≠

0

H

0

:

β

≠

0

H

A

:

β

=

0b) The test statistic value is:

t

=c) The p-value is:d) Based on this, we

Reject

H

0

Fail to reject

H

0e) Which means

There is sufficient evidence to show a that significant correlation exists.

There is not sufficient evidence show that a significant correlation exists.

There is sufficient evidence to show a significant correlation does not exist.

There is not sufficient evidence to show that a significant correlation does not exist.f) The regression equation (in terms of income

x

) is:

ˆ

y

=g) To predict what diameter a child would draw a nickel given family income, it would be most appropriate to:

Use the regression equation

Use the mean

Use the P-Value

Use the residual

34 30

31 22

24 14

25 18

31 25

18 26

18 31

9 3

38 34

24 23

18 16

31 17

16 23

35 24

8 21

25 32

18 20

8 17

17 16

30 19

13 18

31 16

14 20

14 24

15 21

14 25

21 17

23 18

18 16

28 28

29 21

24 25

28 24

16 15

14 19

18 20

25 21

11 20

10 28

23 16

63 21

56 15

70 21

41 19

98 26

48 27

57 22

75 18

46 23

42 16

67 20

68 19

74 18

54 19

64 18

63 12

64 22

70 24

47 18

81 20

64 18

67 20

52 13

93 14

97 24

92 15

45 11

58 17

74 19

46 17

99 25

90 24

91 14

89 11

88 21You can copy the data into StatCrunch by highlighting the data, right-clicking and selecting Copy (or Ctrl + c), then open the StatCrunch window, click on the first cell, and right-clicking and selecting Paste (or Ctrl + v).Test the claim that there is significant correlation at the 0.01 significance level using a linear regression t-test for the slope. Retain at least 3 decimals on all values.a) Identify the correct hypotheses.

H

0

:

r

=

0

H

A

:

r

≠

0

H

0

:

p

L

o

w

=

p

H

i

g

h

H

A

:

p

L

o

w

≠

p

H

i

g

h

H

0

:

μ

=

0

H

A

:

μ

≠

0

H

0

:

β

=

0

H

A

:

β

≠

0

H

0

:

β

≠

0

H

A

:

β

=

0b) The test statistic value is:

t

=c) The p-value is:d) Based on this, we

Reject

H

0

Fail to reject

H

0e) Which means

There is sufficient evidence to show a that significant correlation exists.

There is not sufficient evidence show that a significant correlation exists.

There is sufficient evidence to show a significant correlation does not exist.

There is not sufficient evidence to show that a significant correlation does not exist.f) The regression equation (in terms of income

x

) is:

ˆ

y

=g) To predict what diameter a child would draw a nickel given family income, it would be most appropriate to:

Use the regression equation

Use the mean

Use the P-Value

Use the residual

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