**Assignment 2: Discussion**

You are a data analyst with John and Sons Company. The company has a large number of manufacturing plants in the United States and overseas. The company plans to open a new manufacturing plant. It has to decide whether to open this plant in the United States or overseas.

What is an appropriate null hypothesis to compare the quality of the product manufactured in the overseas plants and the U.S. plants? How would you choose an appropriate level of significance for your statistical test?

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**Hypothesis Testing for Starting a Manufacturing Plant**

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**Hypothesis Testing for Starting a Manufacturing Plant**

“It’s not about ideas. It’s about making ideas happen” is a famous quote by Scott Belsky. According to List et al. (2019), hypothesis testing is an essential statistical method used to make decisions about the validity of an assumption or claim about a population parameter. In starting a manufacturing plant, hypothesis testing can help make informed decisions about the project’s viability by testing various assumptions and claims related to the market demand, production costs, and profitability. According to Levine (2020), one of the key assumptions that can be tested through hypothesis testing is the demand for the product. Before starting a manufacturing plant, knowing if there is sufficient demand for the product in the market is essential. A null hypothesis can be formulated that there is no significant difference between the expected and actual demand, while the alternative hypothesis can be that there is a significant difference. A statistical test can then be conducted to determine if the null hypothesis should be accepted or rejected.

Another important assumption that can be tested through hypothesis testing is the production cost Levine (2020). The cost of production is a critical factor in determining the profitability of a manufacturing plant. Levine (2020) also stated that a null hypothesis could be formulated that the production cost will not exceed a certain threshold, while the alternative hypothesis can be that the production cost will exceed the threshold. A statistical test can be conducted to determine if the null hypothesis should be accepted or rejected. In addition to testing assumptions about demand and production costs, hypothesis testing can also be used to test the profitability of the manufacturing plant (Levine, 2020). A null hypothesis can be formulated that the manufacturing plant will not be profitable, while the alternative hypothesis can be that the manufacturing plant will be profitable. A statistical test can be conducted to determine if the null hypothesis should be accepted or rejected (Levine, 2020). This paper discusses the appropriate null hypothesis to compare the quality of the product manufactured in overseas and U.S. plants? And why would one choose an appropriate level of significance for your statistical test?

The null hypothesis for this comparison would be that the quality of the product manufactured in overseas and U.S. plants is equal. According to Sedgwick et al. (2022), when starting a manufacturing plant, it is essential to determine if the quality of the product manufactured in overseas and U.S. plants is the same. Sedgwick et al. (2022) also stated that to do this; an appropriate null hypothesis can be formulated and tested. This hypothesis can be stated mathematically as H0: μ1 = μ2, where μ1 is the mean quality of the product manufactured in the overseas plants and μ2 is the mean quality of the product manufactured in the U.S. plants. Once the null and alternative hypotheses are established, a statistical test can be conducted to determine if the null hypothesis should be accepted or rejected. The statistical test results can then be used to decide the quality of the product manufactured in overseas and U.S. plants. Thus, the null hypothesis for this comparison would be that the quality of the product manufactured in overseas and U.S. plants is equal.

**Why Would One Choose an Appropriate Level of Significance for the Statistical Test?**

When starting a manufacturing plant, one of the important decisions that must be made is choosing the appropriate level of significance for a statistical test. One reason for choosing an appropriate significance level for the statistical test is that it is the default assumption. According to Vrbin (2020), the significance level is the probability of rejecting the null hypothesis, given that it is true. In other words, the level of risk the decision-maker is willing to accept when deciding whether to reject the null hypothesis. Vrbin also stated that the null hypothesis is the default assumption because it represents the absence of an effect or difference. By assuming that the quality of the product manufactured in the two plants is equal, we are essentially saying that there is no difference in quality unless proven otherwise through statistical evidence (Vrbin, 2020). The appropriate significance level depends on each case’s specific circumstances. In some situations, a higher level of significance may be appropriate. For example, in medical trials where the consequences of a false positive result could be severe, a higher level of significance, such as 0.01, may be used to reduce the risk of making a false positive conclusion (Vrbin, 2020). On the other hand, in some situations, a lower level of significance may be appropriate. For example, in exploratory research, a lower level of significance, such as 0.10, may increase the likelihood of detecting potential relationships (Vrbin, 2020). Thus, one reason for choosing an appropriate level of significance for the statistical test is that it is the default assumption.

Another reason for choosing an appropriate significance level for the statistical test is that the null hypothesis is easier to reject than accept. According to Tendeiro et al. (2019), when a statistical hypothesis test is performed, the significance level sets the threshold for rejecting the null hypothesis, which is the assumption that there is no relationship between the variables being studied. Tendeiro et al. (2019) also stated that the level of significance is typically represented by alpha (α) and is usually set at 0.05, which means that there is a 5% chance that the results of the test are due to random chance and not because of a real relationship between the variables. By setting the level of significance at 0.05, researchers can feel confident that if their test results are significant, it is likely that there is indeed a real relationship between the variables and not just random chance (Tendeiro et al., 2019). However, if the level of significance is set too low, such as 0.01, it becomes much more difficult to reject the null hypothesis, as the threshold for significance becomes stricter; This means that the results of the test may not be significant even if there is a real relationship between the variables, leading to false negatives (Tendeiro et al., 2019). On the other hand, if the level of significance is set too high, such as 0.10, it becomes much easier to reject the null hypothesis, as the threshold for significance becomes more lenient; This means that the results of the test may be significant even if there is not a real relationship between the variables, leading to false positives (Tendeiro et al., 2019). Thus, another reason for choosing an appropriate significance level for the statistical test is that the null hypothesis is easier to reject than accept.

In conclusion, hypothesis testing is a powerful tool that can be used to make informed decisions about starting a manufacturing plant. When starting a manufacturing plant, it is essential to determine if the quality of the product manufactured in overseas and U.S. plants is the same. An appropriate null hypothesis for this comparison would be that the quality of the product manufactured in the two plants is equal. The alternative hypothesis is that the quality is not equal. The null hypothesis for comparing the quality of the product manufactured in the overseas and U.S. plants is equal because it is the default assumption and easier to reject. By testing these hypotheses, a decision can be made about the quality of the product manufactured in the plant.

Levine, M. (2022). A cognitive theory of learning: Research on hypothesis testing. Taylor & Francis.

List, J. A., Shaikh, A. M., & Xu, Y. (2019). Multiple hypothesis testing in experimental economics. Experimental Economics, 22, 773-793.

Sedgwick, P. M., Hammer, A., Kesmodel, U. S., & Pedersen, L. H. (2022). Current controversies: Null hypothesis significance testing. Acta Obstetricia et Gynecologica Scandinavica, 101(6), 624-627. https://doi.org/10.1111/aogs.14366

Tendeiro, J. N., & Kiers, H. A. (2019). A review of issues about null hypothesis Bayesian testing. Psychological methods, 24(6), 774. https://doi.org/10.1037/met0000221

Vrbin, C. M. (2022). Parametric or nonparametric statistical tests: Considerations when choosing the most appropriate option for your data. Cytopathology, 33(6), 663-667. https://doi.org/10.1111/cyt.13174

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