Instructions
Hypothesis Testing and Inference
This assignment focuses on estimation and hypothesis testing with onesample and twosample inferences.
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 zscore table) provided in the course textbook (Table 3—The normal distribution—in the Tables section in APPENDIX) to obtain your responses.
Click here to access the standardized normal distribution table from your course textbook.
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 attentiondeficit/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 ADHDrelated 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.
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. A report template is provided for submission of your work.
Note: Tables 1 and 2 are practice tables with answers. Tables 3 and 4 are the assignment tables for you to work on.
Table 1 (µ = 100 seconds and σ = 10)
Child 
Mean seconds of concentration in an experiment of reading 
zscore 
pvalue 
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)
Child 
Mean seconds of concentration in an experiment of reading 
zscore 
pvalue 
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)
Child 
Mean seconds of concentration in an experiment of reading 
zscore 
pvalue 
1 
75 
0.83 

2 
81 
0.63 

3 
89 
0.37 

4 
99 
0.03 

5 
115 
0.50 

6 
127 
0.09 

7 
138 
1.27 

8 
139 
1.30 

9 
142 
1.40 

10 
148 
1.60 
Table 4 (µ = 100 seconds and σ = 40)
Child 
Mean seconds of concentration in an experiment of reading 
zscore 
pvalue 
1 
75 
0.63 

2 
81 
0.48 

3 
89 
0.28 

4 
99 
0.03 

5 
115 
0.38 

6 
127 
0.68 

7 
138 
0.95 

8 
139 
0.98 

9 
142 
1.05 

10 
148 
1.20 
Click here for a template to provide your answers and submit the assignment.
Refer to the Assignment Resources on this page for Two Independent Samples of tTest to view an example of probability using standard variable and normal distribution tables. The same resource is also available under lecture Estimation and Hypothesis Testing.
Submission Details:
 Name your document doc.
 Submit your document to the Submissions Areaby the due date assigned.
Problem 2: TwoSample Inferences
A twosample inference deals with dependent and independent inferences. In a twosample hypothesis testing problem, underlying parameters of two different populations are compared. In a longitudinal (or followup) study, the same group of people is followed over time. Two samples are said to be paired when each data point in the first sample is matched and related to a unique data point in the second sample.
This problem demonstrates inference from two dependent (followup) samples using the data from the hypothetical study of new cases of tuberculosis (TB) before and after the vaccination was done in several geographical areas in a country in subSaharan Africa. Conclusion about the null hypothesis is to note the difference between samples.
The problem that demonstrates inference from two dependent samples uses hypothetical data from the TB vaccinations and the number of new cases before and after vaccination.
Table 5: Cases of TB in Different Geographical Regions
Geographical regions 
Before vaccination 
After vaccination 
1 
85 
11 
2 
77 
5 
3 
110 
14 
4 
65 
12 
5 
81 
10 
6 
70 
7 
7 
74 
8 
8 
84 
11 
9 
90 
9 
10 
95 
8 
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:
 Construct a onesided 95% confidence interval for the true difference in population means.
 Test the null hypothesis that the population means are identical at the 0.05 level of significance.
Click here to install Minitab Software.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
Submission Details:
 Name your Minitab output file mtw.
 Name your document doc.
 Submit your document to the Submissions Areaby the due date assigned.
Problem 3: CrossSectional Study
In a crosssectional study, the participants are seen at only one point of time. Two samples are said to be independent when the data points in one sample are unrelated to the data points in the second sample.
The problem that demonstrates inference from two independent samples will use hypothetical data from the American Association of Poison Control Centers.
There are two groups of independent data collected in different regions, which also calls for a ttest. The numbers represent the number of recorded cases of poisoning with chemicals in the homes of 100,000 people in two regions.
Table 6: Cases of Poisoning With Chemicals
Year 
Region 1 
Region 2 
1 
150 
11 
2 
160 
10 
3 
132 
14 
4 
110 
12 
5 
85 
10 
6 
45 
11 
7 
123 
9 
8 
180 
11 
9 
143 
10 
10 
150 
14 
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:
 Formulate a null and an alternative hypothesis for a twosided test.
 Conduct the test at the 0.05 level of significance.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
Submission Details:
 Name your Minitab output file mtw.
 Name your document doc.
 Submit your document to the Submissions Areaby the due date assigned.
Additional Materials
View a pdf Transcript of OneTailed and TwoTailed Test
View a pdf Transcript of Minitab Example of Two Independent Samples of tTest
View a pdf Transcript of Minitab Express
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