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.

opatovaL 2021-02-09 Answered

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. Geographical regionsBefore vaccinationAfter vaccination18511277531101446512581106707774888411990910958
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.

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delilnaT
Answered 2021-02-10 Author has 94 answers

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

SampleNMeanStDevSE MeanBefore vaccination1083.1013.084.14After vaccination109.502.640.83
Estimation for Paired Difference
MeanStDevSE Mean95 CI for μdifference73.6012.203.86(64.87, 82.33)
μdifference mean of (Before vaccination - After vaccination)
Test
Null hypothesisH0:μdifference=0Alternative hypothesisH1:μdifference0
TValuePValue19.070.000
The 95% 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.

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