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 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

First, click hereto install Statistical Package for the Social Sciences (SPSS) Software analytical software package.

Click here to access the dataset.

Using SPSS, download the data and perform the analysis, then 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.