The significance of each child's data (insofar as it reflects on the population as a whole, or reflects the population as a whole) decreases as the data becomes more and more dispersed. The fact that the null hypothesis was not rejected in any case after the standard deviation (sigma) reached 20 demonstrates how difficult it can be to make meaningful conclusions when data is very widely spread.
Z Score
Fill in the answers for each table and answer the concluding FOUR questions below. Please round up your z scores to the hundredths spot, two decimals to the right and p values to the thousandths spot three decimals to the right as needed. If the p value is less than .001, please report p < .001. Please note when a value appears in SPSS as .000, it is truly p
Make sure to write out a formal APA statement of conclusion for each child as the instructions state.
µ = 100; =10
Child
Concentration
Z
P
Error
Child
z=
p=
Decision about H0:
Possible Error:
Child
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child
89
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child
99
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 6
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 7
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 8
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 9
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 10
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Report z scores to two decimals and p values to three decimals. If the p value is less than .001, report it as p < .001.
Problem 1
µ = 100
=10
Child
Concentration
z score p value
Decision for H0
error type
1
75
-2.50
0.006
reject
I
2
81
-1.90
0.029
reject
I
3
89
-1.10
0.136
fail to reject
II
4
99
-0.10
0.460
fail to reject
II
5
1.50
0.933
fail to reject
II
6
2.70
0.997
fail to reject
II
7
3.80
0.999
fail to reject
II
8
3.90
0.999
fail to reject
II
9
4.20
0.999
fail to reject
II
10
4.80
0.999
fail to reject
II
Add your 10 APA-style conclusion statements for Problem 1 here.
1. The null hypothesis is rejected and the alternative hypothesis is accepted in its stead.
2. The null hypothesis is rejected and the alternative hypothesis is accepted in its stead.
3. The null hypothesis is not rejected, but continues to be valid.
4. The null hypothesis is not rejected, but continues to be valid.
5. The null hypothesis is not rejected, but continues to be valid.
6. The null hypothesis is not rejected, but continues to be valid.
7. The null hypothesis is not rejected, but continues to be valid.
8. The null hypothesis is not rejected, but continues to be valid.
9. The null hypothesis is not rejected, but continues to be valid.
10. The null hypothesis is not rejected, but continues to be valid.
Which child or children, if any, appeared to come from a significantly different population than the one used in the null hypothesis?
The first two children definitely appear to be of a population significantly different from that of the child used to derive the null hypothesis, and the next three or four might also be from a different population even though the null hypothesis is supported in their individual cases.
PROBLEM #2
Problem 2: µ = 100; =20
Child
Concentration
Z
P
Hypothesis
Error
Child 1
75
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 2
81
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 3
89
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 4
99
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 5
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 6
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 7
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 8
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 9
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 10
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Report z scores to two decimals and p values to three decimals. If the p value is less than .001, report it as p < .001.
Problem 2
µ = 100
=20
Child
Concentration
z score p value
Decision for H0
error type
1
75
-1.25
0.106
fail to reject
II
2
81
-0.95
0.171
fail to reject
II
3
89
-0.55
0.291
fail to reject
II
4
99
-0.05
0.480
fail to reject
II
5
0.75
0.773
fail to reject
II
6
1.35
0.912
fail to reject
II
7
1.90
0.971
fail to reject
II
8
1.95
0.974
fail to reject
II
9
2.10
0.982
fail to reject
II
10
2.40
0.992
fail to reject
II
Add your 10 APA-style conclusion statements for Problem 2 here.
1. The null hypothesis is not rejected, but continues to be valid.
2. The null hypothesis is not rejected, but continues to be valid.
3. The null hypothesis is not rejected, but continues to be valid.
4. The null hypothesis is not rejected, but continues to be valid.
5. The null hypothesis is not rejected, but continues to be valid.
6. The null hypothesis is not rejected, but continues to be valid.
7. The null hypothesis is not rejected, but continues to be valid.
8. The null hypothesis is not rejected, but continues to be valid.
9. The null hypothesis is not rejected, but continues to be valid.
10. The null hypothesis is not rejected, but continues to be valid.
Which child or children, if any, appeared to come from a significantly different population than the one used in the null hypothesis?
No children appeared to be from a significantly different population from the child used to derive the null hypothesis.
PROBLEM #3
Problem 3: µ = 100; =30
Child
Concentration
Z
P
Hypothesis
Error
Child 1
75
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 2
81
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 3
89
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 4
99
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 5
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 6
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 7
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 8
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 9
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 10
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Report z scores to two decimals and p values to three decimals. If the p value is less than .001, report it as p < .001.
Problem 3
µ = 100
=30
Child
Concentration
z score p value
Decision for H0
error type
1
75
-0.83
0.203
fail to reject
II
2
81
-0.63
0.264
fail to reject
II
3
89
-0.37
0.356
fail to reject
II
4
99
-0.03
0.488
fail to reject
II
5
0.50
0.692
fail to reject
II
6
0.90
0.816
fail to reject
II
7
1.27
0.898
fail to reject
II
8
1.30
0.903
fail to reject
II
9
1.40
0.919
fail to reject
II
10
1.60
0.945
fail to reject
II
Add your 10 APA-style conclusion statements for Problem 3 here.
1. The null hypothesis is not rejected, but continues to be valid.
2. The null hypothesis is not rejected, but continues to be valid.
3. The null hypothesis is not rejected, but continues to be valid.
4. The null hypothesis is not rejected, but continues to be valid.
5. The null hypothesis is not rejected, but continues to be valid.
6. The null hypothesis is not rejected, but continues to be valid.
7. The null hypothesis is not rejected, but continues to be valid.
8. The null hypothesis is not rejected, but continues to be valid.
9. The null hypothesis is not rejected, but continues to be valid.
10. The null hypothesis is not rejected, but continues to be valid.
Which child or children, if any, appeared to come from a significantly different population than the one used in the null hypothesis?
No children appeared to be from a significantly different population from the child used to derive the null hypothesis.
PROBLEM #4
Problem 4: µ = 100; =40
Child
Concentration
Z
P
Hypothesis
Error
Child 1
75
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 2
81
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 3
89
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 4
99
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 5
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 6
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 7
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 8
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 9
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Child 10
z=
p=
Decision about H0:
Possible Error:
APA Statement:
Report z scores to two decimals and p values to three decimals. If the p value is less than .001, report it as p < .001.
Problem 4
µ = 100
=40
Child
Concentration
z score p value
Decision for H0
error type
1
75
-0.63
0.264
fail to reject
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