Please respond to the 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