Learn Comparing two groups with Plainmath's Expert Help and Detailed Explanations

Iron is very important for babies' growth. A common belief is that breastfeeding will help the baby to get more iron than formula feeding. To justify the belief, a study followed 2 groups of babies from born to 6 months. With one group babies are breast fed, and the other group are formula fed without iron supplements. Data below shows iron levels of those two groups of babies.

$\begin{array}{|cccc|}\hline Group& Samplesize& mean& Standarddeviation\\ Breast-fed& 23& 13.3& 1.7\\ Formula-fed& 23& 12.4& 1.8\\ DIFF=Breast-Formula& 23& 0.9& 1.4\\ \hline\end{array}$

(1) There are two groups we need to compare for the study: Breast-Fed and Formula- Fed. Are those two groups dependent or independent? Based on your answer, what inference procedure should we apply for this research?

(2) Please perform the inference you decided in (1), and make sure to follow the 5-step procedure for any hypothesis test.

(3) Based on your conclusion in (2), what kind of error could you make? Explain the type of error using the context words for this research

Why is it important that a sample be random and representative when conducting hypothesis testing? Representative Sample vs. Random Sample: An Overview Economists and researchers seek to reduce sampling bias to near negligible levels when employing statistical analysis. Three basic characteristics in a sample reduce the chances of sampling bias and allow economists to make more confident inferences about a general population from the results obtained from the sample analysis or study: * Such samples must be representative of the chosen population studied. They must be selected at random, meaning that each member of the larger population has an equal chance of being chosen. * They must be big enough so as not to bias the results. The optimal size of the sample group depends on the precise degree of confidence required for making an inference. Representative sampling and random sampling are two techniques used to help ensure data is free of bias. These sampling techniques are not mutually exclusive and, in fact, they are often used in tandem to reduce the degree of sampling error in an analysis and allow for greater confidence in making statistical inferences from the sample in regard to the larger group. Representative Sample A representative sample is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicates the larger group according to whatever characteristic or quality is under study. A typical sample mirrors important variables and traits of the large society being studied. Some examples include sex, age, education level, socioeconomic status (SES), or marital status. A larger sample size reduced sampling error and increases the likelihood that the sample accurately reflects the target population. Random Sample A random sample is a group or set chosen from a larger population or group of factors of instances in a random manner that allows for each member of the larger group to have an equal chance of being chosen. A random sample is meant to be an unbiased representation of the larger population. It is considered a fair way to select a sample from a larger population since every member of the population has an equal chance of getting selected. Special Considerations: People collecting samples need to ensure that bias is minimized. Representative sampling is one of the key methods of achieving this because such samples replicate as closely as possible elements of the larger population under study. This alone, however, is not enough to make the sampling bias negligible. Combining the random sampling technique with the representative sampling method reduces bias further because no specific member of the representative population has a greater chance of selection into the sample than any other. Summarize this article in 250 words.

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