# Assignment 2: Practice with Dispersion Essay

Assignment 2: Practice with Dispersion

Problem 1 - **Assignment 2: Practice with Dispersion Essay** introduction. μ = 100 seconds and σ = 10

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Child

Mean Seconds of Concentration (X)

µ

σ

z-score (X – μ)/s

p

Area left to z score

1

75

100

10

-2.50

0.01

0.01

2

81

100

10

-1.90

0.03

0.03

3

89

100

10

-1.10

0.14

0.14

4

99

100

10

-0.10

0.46

0.46

5

115

100

10

1.50

0.07

0.93

6

127

100

10

2.70

0.00

1.00

7

138

100

10

3.80

0.00

1.00

8

139

100

10

3.90

0.00

1.00

9

142

100

10

4.20

0.00

1.00

10

148

100

10

4.80

0.00

1.00

Which child or children, if any, appeared to come from a significantly different population than the one used in the null hypothesis?

Except child 3, 4, and 5 , all children appeared to come from a significantly different population than the one used in the null hypothesis.

Problem 2. μ = 100 seconds and σ = 20

Child

Mean Seconds of Concentration (X)

µ

σ

z-score (X – μ)/s

p

Area left to z score

1

75

100

20

-1.25

0.11

0.11

2

81

100

20

-0.95

0.17

0.17

3

89

100

20

-0.55

0.29

0.29

4

99

100

20

-0.05

0.48

0.48

5

115

100

20

0.75

0.23

0.77

6

127

100

20

1.35

0.09

0.91

7

138

100

20

1.90

0.03

0.97

8

139

100

20

1.95

0.03

0.97

9

142

100

20

2.10

0.02

0.98

10

148

100

20

2.40

0.01

0.99

Which child or children, if any, appeared to come from a significantly different population than the one used in the null hypothesis?

Child 7, 8, 9, and 10 appeared to come from a significantly different population than the one used in the null hypothesis.

Problem 3. μ = 100 seconds and σ = 30

Child

Mean Seconds of Concentration (X)

µ

σ

z-score (X – μ)/s

p

Area left to z score

1

75

100

30

-0.83

0.20

0.20

2

81

100

30

-0.63

0.26

0.26

3

89

100

30

-0.37

0.36

0.36

4

99

100

30

-0.03

0.49

0.49

5

115

100

30

0.50

0.31

0.69

6

127

100

30

0.90

0.18

0.82

7

138

100

30

1.27

0.10

0.90

8

139

100

30

1.30

0.10

0.90

9

142

100

30

1.40

0.08

0.92

10

148

100

30

1.60

0.05

0.95

Which child or children, if any, appeared to come from a significantly different population than the one used in the null hypothesis?

No child appeared to come from a significantly different population than the one used in the null hypothesis.

Problem 4. μ = 100 seconds and σ = 40

Child

Mean Seconds of Concentration (X)

µ

σ

z-score (X – μ)/s

p

Area left to z score

1

75

100

40

-0.63

0.27

0.27

2

81

100

40

-0.48

0.32

0.32

3

89

100

40

-0.28

0.39

0.39

4

99

100

40

-0.03

0.49

0.49

5

115

100

40

0.38

0.35

0.65

6

127

100

40

0.68

0.25

0.75

7

138

100

40

0.95

0.17

0.83

8

139

100

40

0.98

0.16

0.84

9

142

100

40

1.05

0.15

0.85

10

148

100

40

1.20

0.12

0.88

No child appeared to come from a significantly different population than the one used in the null hypothesis.

What happens to the `significance` of each child’s data as the data are progressively more dispersed?

From above four problems with same mean and different standard deviation, it can be seen that as the value of standard deviation increases from σ = 10 to σ = 40, the z score is concentrated more towards center that is around zero (or mean value). Therefore, as the data are progressively more dispersed, there will be less chance of `significance` of each child’s data.