Hello,

I need four responses of at least 175 words each for the below students discussions for this week. Also in the bold below are the questions the students at answering.

**What is hypothesis testing? Explain the general process and the steps included in conducting a hypothesis test? What is the difference between parametric and nonparametric hypothesis testing?**

Student one:

Hypothesis testing is common in math and science, but it is also a useful tool for business mangers, â€˜good hypotheses lead decision-makers to new and better ways to achieve business goals.â€™ (Ogunjimi) Hypothesis testing is a statistical test used to determine whether the hypothesis assumed for the sample of data stands true for the entire population or not. (Hypothesis testing) From our text, we know that the data sets are called the null hypothesis and the alternative hypothesis. The null hypothesis describes an existing theory or a belief. The alternative hypothesis is based on new information provided by sample data. (Evans, 2013)

According to our text, there are five steps in a hypothesis test:

- Formulating the hypothesis to test. This step is where data sets, the Null and the Alternate Hypothesis are defined.
- Selecting a level of significance, which identifies the risk of drawing an incorrect conclusion about the assumed hypothesis that is actually true. Hypothesis testing can result in four possible outcomes. This step demonstrates the risk that the business is willing to take in making an incorrect conclusion.
- Determining a decision rule on which to base a conclusion. This step involves choosing which Test Statistic to use, examples include the one-tailed or two-tailed tests.
- Collecting data and calculating a test statistic; formulating the Decision Rule
- Applying the decision rule to the test statistic and drawing a conclusion. Make the decision to accept or reject the null hypothesis.

Basically, the manager needs to decide what theyâ€™re trying to confirm. Next, they determine the level of risk that is acceptable, should they make a mistake. The third step is deciding how they will make their decision, ie. provide justification. They will then collect the data and apply the selected test to justify their decision. It is a formal process that helps guide managers in testing their ideas, providing risk awareness, and support for their decision.

The parametric test is the statistical test, in which specific assumptions are made about the population parameter. The nonparametric test is defined as the hypothesis test which is not based on underlying assumptions. There are many differences between these two tests, but I think the main difference between them is that the information about the population for the parametric test is completely known, for the nonparametric test, it is unavailable. (Updated, 2017)

I agree that hypotheses testing can be very useful in business. It seems to me they have made the process very scientific, which makes it easy to explain how the manager came to the conclusion, and shows whether it is or isnâ€™t within the identified risk level. However, I donâ€™t think the process guarantees the best conclusion.

Thank you,

# References

Evans, J. R. (2013). *Statistics, Data Analysis, and Decision Making.* Upper Saddle River, New Jersey: Pearson Education Inc.

Frost, J. (n.d.). *Nonparametic Tests vs. Parametric tests*. Retrieved January 21, 2020, from Statistics by Jim: https://statisticsbyjim.com/hypothesis-testing/non…

*Hypothesis testing*. (n.d.). Retrieved January 21, 2020, from Business Jargons: https://businessjargons.com/hypothesis-testing.htm…

Ogunjimi, A. (n.d.). *Small Business Chronicle*. Retrieved January 21, 2020, from How Is a Hypothesis Important in Business?: https://smallbusiness.chron.com/hypothesis-importa…

Updated, S. S. (2017, September 1). Retrieved January 21, 2020, from Key Differences: https://keydifferences.com/difference-between-para…

Student two:

In chapter five I learned that hypothesis testing is a way of collecting data that involves two unidentical things. Evansâ€™s defined hypothesis testing as a process that â€œinvolves drawing inferences about two contrasting propositions (hypotheses) relating to the value of a population parameter, such as a mean, proportion, standard deviation, or variance.

Using the null hypothesis and the alternative hypothesis a conclusion can be made as to whether or not a hypostasis is likely.

The basic process and the steps included in conducting a hypothesis test is to identify the null hypothesis and the alternative hypothesis. Once those items are identified the size of the testing population needs to be determined. The statistical and probability values are then calculated to determining a decision rule-, and lastly applying the decision rule to the test statistic by coming to a conclusion based on the data collected.

Parametric testing is an option that is best used when the population parameter is determined or known. This means that the testing condition must be validated.

nonparametric hypothesis testing is the opposite, the population parameter is not known. nonparametric hypothesis testing is broader and can apply to more situations.

â€œThe assumptions for the nonparametric test are weaker than those for the parametric test, and it has been stated that when the assumptions are not met, it is better to use the nonparametric test (Kitchen, Christina M.R.,).

Evans, J. R. (2013). *Statistics, Data Analysis, and Decision Modeling* (5th ed.). Upper Saddle River, NJ: Prentice Hall.

Nonparametric vs Parametric Tests of Location in Biomedical Research Kitchen, Christina M.R.American Journal of Ophthalmology, Volume 147, Issue 4, 571 – 572

Student three:

Hypothesis testing is basically drawing a conclusion about a population. One is a proposition that describes an already existing position while the other is new information that is gathered from the sample data. The sample data is then used to determine whether or not to reject the null hypothesis, which would mean that the sample data provided enough information to support the alternative hypothesis, or reject the null hypothesis, which means that the sample evidence did not support the null hypothesis (Evans, 2013).

The first step in hypothesis testing is formulating the hypotheses to test. Hypothesis formulation begins by â€œdefining two alternative, mutually exclusive propositions about one or more population parametersâ€ (Evans, 2013, p. 156). The next step would be to figure out the significance level of the test. The level of significance is the risk that can be afforded if an error is made. The levels that are commonly used are .10, .05, and .01 which coincides with the confidence levels of .90, .95 and .99 respectively. Once the significance level is decided on the decision rule is determined. The decision rule is a statement which defines the conditions which determines if the null hypothesis is rejected or not. Lastly, a decision has to be made based upon the hypothesis test whether to accept or reject the null hypothesis.

Nonparametric and parametric tests have their advantages and its differences. â€œThe nonparametric tests do not require that your data follow the normal distributionâ€ (Frost, n.d.). Nonparametric tests are advisably used in instances if the data is not distributed normally. Nonparametric tests would include: 1-sample Sign, 1-sample Wilcoxon, Mann-Whitney test, Kruska-Wallis, Moodâ€™s median test and Friedman test. Parametrics tests would include: 1-sample t-test, 2-sample t-test, One-Way ANOVA, and Factorial DOE with a factor and a blocking variable. The Parametric tests and Nonparametric tests are linked pairs of statistical hypothesis tests. The advantage of using parametric test is the fact that it can provide very trustworthy results even when the data is skew or abnormal, as long as the sample size meets the requirements for the specific test (Frost, n.d.). Parametric tests also have greater statistical power. Meaning, it can detect an effect if it exists. Nonparametric tests assess the median instead of the mean. The mean is not always the better way of determining the central tendency for a sample (Frost, n.d.). Nonparametric test can be used when the sample size is small or isnâ€™t enough to satisfy the sample requirements for the parametric tests.

Evans, J. R. (2013). *Statistics, data analysis and decision modeling* (5th ed.). Cincinnati, OH: Pearson Education

Frost, J. (n.d.). Nonparametric tests vs. parametric tests. Retrieved https://statisticsbyjim.com/hypothesis-testing/nonparametric-parametric-tests/

Student four:

â€œHypothesis testing in statistics is a way for you to test the results of a survey or experiment to see if you have meaningful results.â€ (Statistics How To, 2020) Basically, the test is formed around the survey results. First you must know what a hypothesis is. It is an educated guess. It should be testable by experiment or observation. There are the basic steps to follow when performing hypothesis testing:

- Figure out your null hypothesis (
*Null hypothesis*is what is accepted as being true.) - State your null hypothesis
- Choose what kind of test you need to perform
- Either support or reject the null hypothesis

(Statistics How To, 2020)

*Parametric hypothesis tests* assume underlying statistical distribution in the data. â€œParametric test is more able to lead to a rejection of H0. Most of the time, the p-value associated to a parametric test will be lower than the p-value associated to a nonparametric equivalent that is run on the same data.â€ (XLSTAT, 2019)

*Nonparametric hypothesis tests *do no rely on any distribution. This type of test is more â€œrobustâ€, meaning they are â€œvalid in a broader range of situations.â€ (XLSTAT, 2019)

References

Statistics How To. (2020). Hypothesis Testing. Retrieved from https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesis-testing/

XLSTAT. (2019). What is the difference between a parametric and a nonparametric test? Retrieved from https://help.xlstat.com/s/article/what-is-the-difference-between-a-parametric-and-a-nonparametric-test?language=en_US