Improve Your Understanding of College Level Statistics Problems

The equation $a=50h+50$ represents the amount a that an air-conditioning repair company charges for h hours of labour. Make a table and sketch a graph of the equation

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.

Aurora intends to take part in a competition during her school's field day where she must finish tasks at several stations as quickly as she can. She's practicing and timing herself as she completes each station to get ready for the competition. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. ${\displaystyle (1,3),(2,6),(3,12),(4,24)}$
Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5.
Part C: Use an explicit formula to find the time she will complete the 9th station.