**Imagine that your 6-year-old goddaughter wants to know**what you are learning in school. How would you explain binomial and Poisson probability distributions to her in a simple, relatable way?- Compare the different types of random sampling methods and include references for your research. Describe examples in which stratified sampling and cluster sampling should be used. Does God provide sampling methods? Explain.
- Define the differences between a finite population and an infinite population. Provide a real-life example of each. Why are these terms important to business statistics? Use facts to support your response.
- Explain how the level of significance and sample size influence hypothesis testing results. Provide an example and explain how they might impact business decisions. Be sure to give references.

**Sample Answer**

**Discussion Questions**

**Question C**

**Imagine that your 6-year-old goddaughter wants to know what you are learning in school. How would you explain binomial and Poisson probability distributions to her in a simple, relatable way?**

Binomial Probability is all about having only two options or results (Anderson et al, 2021). For examples, we can say that;

- During your exam, the instruction says “TRUE or FALSE”. There can only be two choices which is either true or false in each question.
- Tossing a coin- In tossing a coin, there are only two possible results, it could be a head or a tail and no other results possible.
- If your teacher checks the answers, there are two possible outcomes for each question, it is either right or wrong.

For Poisson Probability, since it is a measure of how many times an event is likely to occur (Anderson et al, 2021), then we can say:

- In a toy store, there could be different customers in 1 hour. There could be 45 different/ unique customers, and 5 customers that comes back within the very hour.
- In a randomly selected week, how possible it is to have 4 accidents in the park.
- In manufacturing barbie dolls, there could be 15 defective dolls out of 1,000. So, what could be the possibility of picking a defective doll out of 1,000 dolls.

**References**

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2021). *Essentials of Modern Business Statistics with Microsoft Office Excel* (8th ed.). Cengage. ISBN-13: 9780357131664

**Question D**

**Compare the different types of random sampling methods and include references for your research. Describe examples in which stratified sampling and cluster sampling should be used. Does God provide sampling methods? Explain.**

Random sampling method are probability sampling methods which allows random selection. If the sample is a good representation of the entire population, then random sampling may help in making statistical inferences about the entire population (Etikan & Bala, 2017). There are four types of random sampling methods namely;

Simple Random Sampling: When any entity of the population has an equal chance of being selected, it is called simple random sampling. For instance, random number generator. The pro is that there is no hidden bias. The con is that there are lesser chances of minority element to be represented in the sample (Anderson et al., 2021; Etikan & Bala, 2017).

Systematic Sampling: When the sampling is done where the entities of the population are chosen at regular intervals, like series, it is called Systematic Sampling. For instance, taking out every 7th entity from a population. The pro is that it is an easier method and easy to implement. The con is that it may lead to a skew in the sample (Anderson et al., 2021; Etikan & Bala, 2017).

Stratified Sampling: When a population is divided into strata’s (or sub-groups) and then use either random sampling or systematic sampling to get the sample. For instance, diving the population into income groups and then taking sample from them. The pro is that it eliminates chance error and ensures equal representation of the strata. The con is that it is difficult to implement (Anderson et al., 2021; Etikan & Bala, 2017).

Cluster Sampling: When a population sample is divided into clusters which has comparable or identical characteristics as the entire population. For instance, selecting only one of the 10 schools to collect the data. One school can represent a cluster. The pro is that it is the best representation of the entire population. The con is that it is difficult to implement (Anderson et al., 2021; Etikan & Bala, 2017).

Yes, God provides sampling methods. In the Holy Bible, God used sampling method to choose his prophets such as Daniel, Ezekiel, Jeremiah, Isaiah, and among others. Besides, He chose Israel (Jewish) as His people among other people to worship only Him as well as accomplish the mission of proclaiming His truth to other World’s nations.