# Z scores, Z statistics, p-value and APA format

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Given the research scenario, data points, set of population parameters and alpha set at p = .05, generate the correct:

- Pair of hypotheses for each data point

- A z statistic and p value for each data point

- Decision about the null hypothesis for each data point

- APA-formatted statement of results for each data point

Please 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

Problem 3: µ = 100 ; σ =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 5 115 z= p= Decision about H0: Possible Error:

APA Statement:

Child 6 127 z= p= Decision about H0: Possible Error:

APA Statement:

Child 7 138 z= p= Decision about H0: Possible Error:

APA Statement:

Child 8 139 z= p= Decision about H0: Possible Error:

APA Statement:

Child 9 142 z= p= Decision about H0: Possible Error:

APA Statement:

Child 10 148 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

σ =30

Child Concentration z score p value

1 75

2 81

3 89

4 99

5 115

6 127

7 138

8 139

9 142

10 148

Add 10 APA-style conclusion statements for Problem 3 here.

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

________________________________________

PROBLEM #4

Problem 4: µ = 100 ; σ =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 5 115 z= p= Decision about H0: Possible Error:

APA Statement:

Child 6 127 z= p= Decision about H0: Possible Error:

APA Statement:

Child 7 138 z= p= Decision about H0: Possible Error:

APA Statement:

Child 8 139 z= p= Decision about H0: Possible Error:

APA Statement:

Child 9 142 z= p= Decision about H0: Possible Error:

APA Statement:

Child 10 148 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

σ =40

Child Concentration z score p value

1 75

2 81

3 89

4 99

5 115

6 127

7 138

8 139

9 142

10 148

Add 10 APA-style conclusion statements for Problem 4 here.

Which child or children, if any, 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?

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##### Solution Summary

This solution is comprised of a detailed explanation of Z scores, Z statistics, p-value and APA format. This solution mainly discussed above 2 questions in which we defined null and alternative hypothesis, calculating the z statistics and p-value and provided the decision about the null hypothesis in APA format. Full calculations are shown in each 10 sub parts of these 2 questions for better clarity.

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