# To explain:Whether the samples are independent or dependent.

Question
Significance tests
To explain:Whether the samples are independent or dependent.

2021-03-07
Justification:
In this study the researcher has randomly selected 8 subjects to determine about the effectiveness of the pain medication. First the eight subjects are asked to give the scale about the pain and after one hour the same subjects are asked to give the scale based on the pain medication. This implies that the same subjects are treated twice for the study and the scale is recorded, and the samples are dependent samples.
Thus, the samples are dependent samples.

### Relevant Questions

Solve the system. If the system does not have one unique solution, also state whether the system is onconsistent or whether the equations are dependent.
2x-y+z=-3
x-3y=2
x+2y+z=-7
Whether the provided P-values are statistically significant or not.

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. $$\begin{array}{|c|c|} \hline Geographical\ regions & Before\ vaccination & After\ vaccination\\ \hline 1 & 85 & 11\\ \hline 2 & 77 & 5\\ \hline 3 & 110 & 14\\ \hline 4 & 65 & 12\\ \hline 5 & 81 & 10\\\hline 6 & 70 & 7\\ \hline 7 & 74 & 8\\ \hline 8 & 84 & 11\\ \hline 9 & 90 & 9\\ \hline 10 & 95 & 8\\ \hline \end{array}$$
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following: Construct a one-sided $$\displaystyle{95}\%$$ 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.

If a report states that certain data were used to reject a given hypothesis, would it be a good idea to know what type of test (one-tailed or two-tailed) was used? Explain.
Critical Thinking: One-Tailed versus Two-Tailed Tests For the same data and null hypothesis, is the P-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain.
To explain:The purpose of the study.
For the same data, null hypothesis, and level of significance, if the conclusion is to reject $$H_{0}$$ based on a two-tailed test, do you also reject Ho based on a one-tailed test? Explain.
c) The $$\displaystyle{x}^{{{2}}}$$ distribution is used for making inferences about two population variances.