Problem : Two-Sample Inferences
A two-sample inference deals with dependent and independent inferences. In a two-sample hypothesis testing problem, underlying parameters of two different populations are compared.
In a longitudinal (or follow-up) 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 (follow-up) 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 sub-Saharan 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: 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
|
|
|
84
|
11
|
Table (μ = 100 seconds and σ = 40)
|
Child
|
Mean seconds of concentration in
an experiment of reading
|
z-score
|
p-value
|
|
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
|
|
Refer to the Assignment Resources on this page for Two Independent Samples of t-Test 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.
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:
• Construct a one-sided 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.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
Problem: Cross-Sectional Study
In a cross-sectional 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 Mest. The numbers represent the number of recorded cases of poisoning with chemicals in the homes of 100,000 people in two regions.
Table: 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 two-sided test
• Conduct the test at the 0.05 level of significance.