Probability Using Standard Variable z and Normal Distribution Tables Variables are the things we measure. A hypothesis is a prediction about the relationship between variables. Variable
This assignment focuses on estimation and hypothesis testing with one-sample and two-sample inferences. The first part you will make tables and not use SPSS.
The essence of parametric testing is the use of standard normal distribution tables of probabilities. For each exercise, there will be a sample problem that shows how the calculations are done and at least one problem for you to work out.
For the first assignment, you will not need any statistical software. However, you will use a standardized normal distribution table (a z-score table) provided in the course textbook (Table 3—The normal distribution—in the Tables section in APPENDIX) to obtain your responses.
Problem 1:
Probability Using Standard Variable z and Normal Distribution Tables
Variables are the things we measure. A hypothesis is a prediction about the relationship between variables. Variables make up the words in a hypothesis.
In the attention-deficit/hyperactivity disorder's (ADHD's) hypothetical example provided in the tables below, the research question was: What is the most effective therapy for ADHD? One of the variables is type of therapy. Another variable is change in ADHD-related behavior, given exposure to therapy. You might measure change in the mean seconds of concentration time when children read. This experiment is designed to obtain children's concentration times while they read a science textbook and to find out whether the therapy used worked on any of the children.
Note: Tables 1 and 2 are practice tables with answers. Tables 3 and 4 are the assignment tables for you to work on. Use the template attached below to provide and submit your assignment answers for Tables 3 and 4.
Table 1 (µ = 100 seconds and σ = 10)- Practice tables
Child | Mean seconds of concentration in an experiment of reading | z-score | p-value |
1 | 75 | -2.50 | 0.0 |
2 | 81 | -1.90 | 0.0 |
3 | 89 | -1.10 | 0.1 |
4 | 99 | -0.10 | 0.4 |
5 | 115 | 1.50 | 0.0 |
6 | 127 | 2.70 | 0.0 |
7 | 138 | 3.80 | <0.0 |
8 | 139 | 3.90 | <0.0 |
9 | 142 | 4.20 | <0.0 |
10 | 148 | 4.80 | <0.0 |
Table 2 (µ = 100 seconds and σ = 20)- Practice tables
Child | Mean seconds of concentration in an experiment of reading | z-score | p-value |
1 | 75 | -1.25 | 0.1 |
2 | 81 | -0.95 | 0.1 |
3 | 89 | -0.55 | 0.2 |
4 | 99 | -0.05 | 0.4 |
5 | 115 | 0.75 | 0.2 |
6 | 127 | 1.35 | 0.0 |
7 | 138 | 1.90 | 0.0 |
8 | 139 | 1.95 | 0.0 |
9 | 142 | 2.10 | 0.0 |
10 | 148 | 2.40 | 0.0 |
Table 3 (µ = 100 seconds and σ = 30)- Table you will work on for assignment
Child | Mean seconds of concentration in an experiment of reading | z-score | p-value |
1 | 75 |
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2 | 81 |
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3 | 89 |
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4 | 99 |
|
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5 | 115 |
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6 | 127 |
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7 | 138 |
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8 | 139 |
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9 | 142 |
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10 | 148 |
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Use the stated µ and σ to calculate probabilities of the standard variable z to get the value of p (up to three decimal places). In addition, respond to the following questions for each pair of parameters:
- 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?
In addition to the above, write a formal statement of conclusion for each child in APA style using the 7th edition of the APA Publication Manual. A report template is provided for submission of your work.
Table 4 (µ = 100 seconds and σ = 40)- Table you will work on for assignment
Child | Mean seconds of concentration in an experiment of reading | z-score | p-value |
1 | 75 |
|
|
2 | 81 |
|
|
3 | 89 |
|
|
4 | 99 |
|
|
5 | 115 |
|
|
6 | 127 |
|
|
7 | 138 |
|
|
8 | 139 |
|
|
9 | 142 |
|
|
10 | 148 |
|
|
Use the stated µ and σ to calculate probabilities of the standard variable z to get the value of p (up to three decimal places). In addition, respond to the following questions for each pair of parameters:
- 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?
In addition to the above, write a formal statement of conclusion for each child in APA style using the 7th edition of the APA Publication Manual. A report template is provided for submission of your work.
