# Assignment 2: Practice with Dispersion Essay

Assignment 2: Practice with Dispersion

Problem 1. 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

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.

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.

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