# 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.

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.
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following: Construct a one-sided $95\mathrm{%}$ 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.

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Paired T-Test and CI: Before vaccination, After vaccination
Descriptive Statistics

Estimation for Paired Difference

${\mu }_{difference}$ mean of (Before vaccination - After vaccination)
Test

$\begin{array}{|cc|}\hline T-Value& P-Value\\ 19.07& 0.000\\ \hline\end{array}$
The $95\mathrm{%}$ confidence interval for the true difference in population means is between 64.87 and 82.33.
Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis. Therefore, we have insufficient evidence to conclude that the population means are identical at the 0.05 level of significance.