Please respond to the discussions with reference

Discussion 1

Explainwhen a z-test would be appropriate over a t-test.

Thez and t-test are both used in hypothesis testing; t-tests are usedin a population of unknown standard deviation and a sample size of< 30. They are also used to compare two different samples anddetermine if there is a significant difference between the twosamples. Z-tests are used in a sample size of >30; they areused to determine whether two population means are different whenthe variances are known, and the sample size islarge.("Statistics How To," 2017)

References

Statisticsfor the rest of us. (2017). Retrieved from http://www.statisticshowto.com/what-is-cluster-sam…

Discussion 2

The T-test is most commonly, a significance test of the difference betweenmeans based on the t distribution. other applications include (a)testing the significance of the difference between a sample mean and ahypothesized value of the mean and (b) testing a specific contrastamong means.

Z-Test is a statistical test used to determinewhether two population means are different when the variances areknown and the sample size is large. The Z-test statistic isassumed to have a normal distribution, and nuisance parameters such asstandard deviation should be known for an accurate Z-test tobe performed.

A Z-test should be used when you are trying to determine whether topopulation means are different whrn the variances are known and thesample size is large.

References

Logic of Hypothesis Testing, https://lc-ugrad3.gcu.edu/learningPlatform/externa…

Https://Www.Investopedia.Com/Terms/Z/Z-Test.Asp

Discussion 3

T-test is usedto examine the differences between the means of two groups. Forexample. In an experiment you may want to compare the overall meanfor the group which the manipulation took place vs a control group.A z test is used to determine whether two population means aredifferent when the variances are known and the sample size is large.The test statistic is assumed to have a normal distribution, andnuisance parameters such as standard deviation should be known foran accurate z test to be performed.

A one-samplelocation test, two sample location test, paired differences test andmaximum likelihood estimate are example of test that can beconducted as z tests. Z-tests are closely related to t-tests, butt-tests are best performed when an experiment has a small samplesize. Also, t tests assume the standard deviation is unknown, whilez-tests assume is it is known. If the standard deviation of thepopulation is unknown, the assumption of the sample varianceequaling the population variance is made (Skaik, 2015).

References

Skaik, Y.(2015). The bread and butter of statistical analysis"t-test": Uses and misuses. US National Library of Medicine.

Discussion 4

A z-test and a t-test are statistical methods usingdata analysis. A z-test is statistical calculation that canbe used to determine whether two population means are differentwhen the variances are known and the sample size is large. Thez-test shows you how far, in standard deviations, a data point is fromthe mean or average of a data set. A z-test is used for largesample( n>30). Z test can be helpful when we want totest a hypothesis. generally, they are most useful when the standarddeviation is known.

A t-test is an analysis of two populations means through the use ofstatistical examination; a t-test with two samples is commonly usedwith small sample sizes, testing the difference between the sampleswhen the variances of two normal distributions are notknown. Usually, t-tests are most appropriate when dealing withproblems with a limited sample size (n < 30).

Reference

Z-test/ T-test.Retrieved from https://www.investopedia.com/terms/z/z-test.asp

Discussion 5

he t-test and z-test are both used in hypothesis testing, but thereare times when using one is more appropriate over the other. The bestinstance to use a t-test is when the sample size is less than 30, andyou have an unknown standard deviation of the population. Inorder to use the z-test you must know the standard deviation of thepopulation and the sample size must be above 30. A z-test will tellyou how many standard deviations from the mean your result is (T-Scorevs. Z-score, 2018).

T-score vs. Z-score: What's the Difference. (2018, January).Retrieved March 5, 2018, from https://www.statisticshowto.com

Discussion 6

Before you run any statistical test, you must first determineyour alpha level, which is also called the“significance level.” By definition,the alpha level is the probability of rejecting thenull hypothesis when the null hypothesis is true.Translation: It's the probability of making a wrongdecision. The smaller the alpha level, the smaller the areawhere you would reject the null hypothesis. Scientists have foundthat an alpha level of 5% is a good balance between these two issues.

If in starting a new program of research for a new drug and thedrug has no harmful side effects, and you want to reduce the chancesof missing an important effect especially since at this point yourprocedures may be relatively unrefined, then you may want toincrease your alpha level to say .10.

That is, your experiment is designed in a way that you have a10% chance of a false positive. It doesn't matter if you misapplythis drug. It's not going to hurt anybody. So, on the one hand, youmay want to have a .01 a point .001 alpha level if the drug hasnasty side effects. Or, you may want to have a .10 alpha level ifyou are doing a pilot study.

What if this drug is for a horrific disease, a crippling diseaseor a life threatening disease? Well, you don't want to do anexperiment that causes you to miss the good drug. Assume it is avery devasting disease. You've got a chance to do something aboutit. So you want to make sure that if the drug works you don't missit. Well you could try to reduce the beta error, to .1 instead of.2. That is increase your power from .8 to .9 maybe .95, whatever ittakes to do that kind of thing. Of course, increasing alphaincreases power, so that is one of your alternatives.

References

Alphas, P-Values, and Confidence Intervals, Oh My! | Minitabblog.minitab.com/blog/michelle-paret/alphas-p-values-confidence-intervals-oh-my