Essay Sample with Some Statistics Questions

Explain when a z-test would be appropriate over a t-test

Being that A Z-test form part of any statistical test for which the distribution of the test statistics under the null hypothesis, there are high chances that the z- test can be approximated through normal distribution (Montgomery, 2017). This is actually because of the central limit theorem that is making the many test statistics to be approximately normally distributed for great samples.

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A T-test is significant in the handling of small samples that exist in the range of (n<30) while a Z test is appropriate when one is handling moderate to large samples for example one that fall in the range of (n>30). On the other hand, when it comes to adaptability, a T-test is viewed to be more adaptable than the Z- test since Z test will in the most cases require certain conditions to be entirely reliable. On the other hand T gain efficiency in many cases since it has various approaches that will suit most of the needs and in most cases; T-test is in most cases used than the Z-tests.

Section 2

Researchers routinely choose an alpha level of 0.5 for testing their hypotheses. What exactly are some of the experiments that one can use in lowering the alpha level (for example, 0.01) and what are some cases in which one might accept a higher level?

Each alpha level has a relationship, and it's normally dependent on some of the circumstances that are surrounding a specific study. For example, if one is conducting a study on cancer, conducting a cancer test would create a chance to determine whether I should do away with the cancerous organ, and I would like to set the cancer level quite stringent at 0.001. Technically it is important not to remove the organ if the organ is cancer free (Greenland, Rothman & Altman, 2016). However, in the case where alpha might be raised to 0.1, then the variance will be entirely different. In the case where one is trying to test whether a mood therapy has a great impact, the alpha can be raised to 0.25 on finding my impact even though chances are increased on coming up with type I error (Cesarini,2018). This is the reason as to why one should understand statistics to make essential decisions. One major reason as to why one will raise the type I error is if the sample size is limited, or if money is not available that ensure doing the study at the 0.05 level. It is also important to note that the study is not accepted in general if it is at 0.1 more, in a case where the sample size was reasonable (Dytham, 2011).

Reference

Benjamin, D. J., Berger, J. O., Johannesson, M., Nosek, B. A., Wagenmakers, E. J., Berk, R., ... & Cesarini, D. (2018). Redefine statistical significance. Nature Human Behaviour, 2(1), 6.

Dytham, C. (2011). Choosing and using statistics: a biologist's guide. John Wiley & Sons.

Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European journal of epidemiology, 31(4), 337-350.

Montgomery, D. C. (2017). Design and analysis of experiments. John wiley & sons.