Download What are the five steps used in hypothesis testing? The first step is to

What are the five steps used in hypothesis testing?
The first step is to state the research question. This is usually stated in words without any fancy
mathematical or statistical notation. It is essentially a question that you are trying to answer in your
research. For example, if you were studying the average weight of residents of California and trying
to determine if their weight is above the national average, your research question might be “Is the
average weight of California residents greater than 170 pounds?”
The second step is to specify the null and alternative hypothesis. Here, you state what the
conventional wisdom is about the population parameters you are studying as the null hypothesis and
the alternative hypothesis would be the what you are trying to prove. Continuing with the example
above, the null hypothesis is: The average weight of California residents is equal to 170 pounds. The
alternative hypothesis is that the average weight of California residents is greater than 170 pounds.
The third step is to calculate the test statistic. You will need to choose the test statistic that is most
appropriate for the data you are analyzing. The test statistic could include the Z-score, a T-score, or
many other test statistics. Continuing with the example above, you would select the Z-score if you
knew the standard deviation of the weights of the population (required for the Z test).
The fourth step is to compute the probability of observing the test statistic or stating the rejection
region. In this step you calculate the p-value associated with your test-statistic calculated in step 4.
Alternatively, but equivalently, you could determine the rejection region of the test statistic.
The
rejection regions is simply the value of the test statistic that when exceed, would result in a rejection
of the null hypothesis.
The final step is to state your conclusion. If you discovered for example that your p-value calculated
in the previous step was very small (e.g. .0001), would you state that there is sufficient evidence to
support rejection of the null hypothesis and conclude that the average weight of California residents is
larger than the average weight of the population of the US.
How do you decide on an alpha significance level? Give an example.
You select a specific alpha level to ensure that you do not falsely reject the null hypothesis when the
null hypothesis is true. Typically the alpha region is selected to be .01 or .05. This means, that, if
you reject the null hypothesis based upon your test statistic, the chances of the null hypothesis being
true (and hence falsely rejected) is 1% or 5% (depending upon the choice of alpha). If, rejecting the
null hypothesis when the null hypothesis is true would be catastrophic, you would likely adjust your
alpha level to be smaller to reduce the chances that you falsely reject the null hypothesis. Continuing
with the weight example, you would likely set the alpha level around .05, as falsely rejecting the null
hypothesis is unlikely to have catastrophic consequences.
Why would you use a z test rather than a t test? Which do you think you will use more
often? Why?
A t-test is more likely to be used than a z-test, because use of the z-test has more restrictions. For
example, the z-test requires a large sample or that the population standard deviation is known. In
practice the population standard deviation is rarely known, and it has to be estimated from your data.
When you estimate the standard deviation, it is appropriate to use a t-test.
When is it appropriate to use a one-tailed test versus a two-tailed test? Does direction of
the test affect statistical significance? Explain.
You use a one-tailed test when you are specifying that the alternative hypothesis is in a specific
direction, either larger or smaller, than the null hypothesis. For example in the example that we are
using, the test would be a one-tailed test as we are stating our alternative hypothesis is that the
weight of California residents is GREATER than the average weight. If our alternative hypothesis had
just indicated that the weight was different (not necessarily greater than or less than, but one or the
other of these), then we would use a two-tailed test. If you use a one sided test the rejection region
is easier to object, because the probabilities associated with the of the rejection region are
concentrated at one tail of the distribution. However, if you use a two sided test, the probability of
the rejection region is split between both ends of the distribution tails.
Why is it more ethical to decide on the tails of the test before collecting and analyzing the
data?
It is more ethical to decide on the tails of the test before analyzing the data as one could simply select
the tail (either one sided or two sided) that makes it easiest to reject the null hypothesis. For
example, a statistician that didn’t select the tails of the test before collecting data might collect the
data and then calculate a test statistic. If the test statistic was not rejected using a two-sided test,
the unethical statistician might then switch to using a one-tailed test hoping that the one-tailed test
results in a rejection of the null hypothesis. This is poor use of the scientific method, because the
statistician is actually modifying the test to support his hopes of a rejection of the null hypothesis.