statistic discussion response 1 – www.savvyessaywriters.net
statistic discussion response 1 – www.savvyessaywriters.net
Please write responses to these 6 discussions with reference
Discussion 1
Explain when a z-test would be appropriate over a t-test.
The z and t-test are both used in hypothesis testing; t-tests are used in a population of unknown standard deviation and a sample size of < 30. They are also used to compare two different samples and determine if there is a significant difference between the two samples. Z-tests are used in a sample size of >30; they are used to determine whether two population means are different when the variances are known, and the sample size is large.(“Statistics How To,” 2017)
References
Statistics for 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 between means based on the t distribution. other applications include (a) testing the significance of the difference between a sample mean and a hypothesized value of the mean and (b) testing a specific contrast among means.
Z-Test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The Z-test statistic is assumed to have a normal distribution, and nuisance parameters such as standard deviation should be known for an accurate Z-test to be performed.
A Z-test should be used when you are trying to determine whether to population means are different whrn the variances are known and the sample 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 used to examine the differences between the means of two groups. For example. In an experiment you may want to compare the overall mean for the group which the manipulation took place vs a control group. A z test is used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution, and nuisance parameters such as standard deviation should be known for an accurate z test to be performed.
A one-sample location test, two sample location test, paired differences test and maximum likelihood estimate are example of test that can be conducted as z tests. Z-tests are closely related to t-tests, but t-tests are best performed when an experiment has a small sample size. Also, t tests assume the standard deviation is unknown, while z-tests assume is it is known. If the standard deviation of the population is unknown, the assumption of the sample variance equaling 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 using data analysis. A z-test is statistical calculation that can be used to determine whether two population means are different when the variances are known and the sample size is large. The z-test shows you how far, in standard deviations, a data point is from the mean or average of a data set. A z-test is used for large sample( n>30). Z test can be helpful when we want to test a hypothesis. generally, they are most useful when the standard deviation is known.
A t-test is an analysis of two populations means through the use of statistical examination; a t-test with two samples is commonly used with small sample sizes, testing the difference between the samples when the variances of two normal distributions are not known. Usually, t-tests are most appropriate when dealing with problems 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 there are times when using one is more appropriate over the other. The best instance to use a t-test is when the sample size is less than 30, and you have an unknown standard deviation of the population. In order to use the z-test you must know the standard deviation of the population and the sample size must be above 30. A z-test will tell you how many standard deviations from the mean your result is (T-Score vs. 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 determine your alpha level, which is also called the “significance level.†By definition, the alpha level is the probability of rejecting the null hypothesis when the null hypothesis is true. Translation: It’s the probability of making a wrong decision. The smaller the alpha level, the smaller the area where you would reject the null hypothesis. Scientists have found that 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 the drug has no harmful side effects, and you want to reduce the chances of missing an important effect especially since at this point your procedures may be relatively unrefined, then you may want to increase your alpha level to say .10.
That is, your experiment is designed in a way that you have a 10% chance of a false positive. It doesn’t matter if you misapply this drug. It’s not going to hurt anybody. So, on the one hand, you may want to have a .01 a point .001 alpha level if the drug has nasty side effects. Or, you may want to have a .10 alpha level if you are doing a pilot study.
What if this drug is for a horrific disease, a crippling disease or a life threatening disease? Well, you don’t want to do an experiment that causes you to miss the good drug. Assume it is a very devasting disease. You’ve got a chance to do something about it. So you want to make sure that if the drug works you don’t miss it. 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 it takes to do that kind of thing. Of course, increasing alpha increases 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
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