Assignment:
Hypothesis Testing Software programs include SPSS and SAS
1) Hypothesis Testing
Hypothesis testing is a well-structured process that consists of several logical steps, and it aims at refining a business decision.
Hypothesis testing is a quite common technique used by researchers.
With regard to hypothesis testing, answer the following questions.
Give a business example on each of the two possible cases of hypothesis testing software programs SPSS and SAS. Do you think the rejection region will be different in each one of the three cases? Why? Why not?
These would be representing a left-tailed test, a two-tailed test, and a right-tailed test. Also, how would you measure a 5% rise in sales? Please review my examples below.
Hypothesis Testing
Guidelines -- Hypothesis Testing Steps:
1. State H0 and Ha.
2. Specify the level of significance alpha a.
3. Determine the test statistic, either z or t. Find the test statistic using the given data.
4. Find the P-value or the critical value(s) z0 or t0. Use the method specified in the problem statement.
5. Define the rejection region using either the P-value method or critical values from the Normal distribution.
6. Make a decision to reject or fail to reject the null hypothesis.
7. Interpret the decision in the context of the original claim.
A researcher is asking a question that needs to be answered but before we get to the statistical data we need to narrow down and simplify this into two competing claims or hypothesis. This usually begins with a theory that's believed to be true or it's going to be the basis for argument. This means we have theory and we're trying to prove it right or wrong. So you need two hypotheses for consideration; one being what you believe to be true and the other being the basis for the argument.
How does a researcher determine which level of significance to use?
The goal is to know what the lowest possibility for error in the testing. Essentially the researcher needs to understand and determine what the margin of error will be on the test and the significance is usually 0.05 but it could be higher and if so it needs to be communicated.
What software programs can be used to compute these tests? Where is the critical test value found?
Statistical packages like Minitab, SAS, and SPSS (Cooper & Schindler, 2011) are a few software programs one can use for computing these tests. Depending on the complexity of the tests, MS Excel or other basic spreadsheet programs may be sufficient for computing these tests. Statistical software has the advantage of being preprogrammed with the critical value tables, which allows the software to determine what the critical value is and its significance (Cooper & Schindler, 2011). When calculated manually, critical value tables can be found in numerous statistical textbooks (see Appendix A-2 in Cooper & Schindler, 2011). "For most tests if the calculated value is larger than the critical value, so we reject the null hypothesis" (Cooper & Schindler, 2011, p. 462).
The actual rejection region will change depending upon the level of significance that one is looking for. For example, GMC decides to test the hypothesis that broad white sidewall tires would increase sales on their Yukon Denali. After obtaining data, it is determined that t (10) = 2.165 on a one-tailed test. If GMC decided that α = 0.10, which means they want a 90% certainty level, the t score would be well within the region of acceptance. The same would occur if GMC used α = 0.05 or 95%. However, if they decided for a certainty level of 99%, or α = 0.01, then the t score would fall within the rejection region of the critical value curve.
How can one determine if the null hypothesis should be rejected?
Statistical significance is used to reject or not reject the null hypothesis. A hypothesis is an explanation or theory that a researcher is trying to prove. The null hypothesis typically holds that the factors at which a researcher is looking have no effect on differences in the data or that there is no connection between the factors. Statistical significance is usually written, for example, as t=1.98, p<.05. Here, "t" stands for the t-value obtained from the sample data and "p<.05" means that the probability of an event occurring by chance is less than 5 percent. These numbers would cause the null hypothesis to be rejected. For a two-tailed test, if alpha is equal to .05, the critical t-value is most likely 1.96, depending on the sample size.
Give a business example on each of the two possible cases of hypothesis testing. Do you think the rejection region will be different in each one of the three cases? Why? Why not?
Three examples would be;
1. An automobile manufacturer claims the average life of their battery is more than 48 months. The null hypothesis would be that the batter life is less than or equal to 48 months. The claim is in the alternative hypothesis, which states that the average batter life is greater than 48 months, which translates to a right-tailed test.
2. The same manufacturer says the mean weight of an item is less than 60 pounds. Here, I would use a null hypothesis that the population mean is greater than or equal to 60 pounds. The claim is in the alternative hypothesis (weight is less than 60 pounds). For this class, the equality sign will always appear in the null hypothesis.
3. A truck manufacturer says their trucks don't use more than 5 gallons of gas per mile. The null hypothesis would be that the mean mpg is equal to 5. The alternative hypothesis is that the mean mpg is not equal to 5, so this is a two-tailed test.
The rejection region will be different for all three because "The area under the sampling distribution curve that defines an extreme outcome is called the rejection region" (Doane & Seward, 2010, pg. 350) this area is different in all three scenarios therefore it will be a different outcome for all three.
References
References
Cooper, D. & Schindler, P. (2010). Business research methods. New York: McGraw-Hill
Doane, D. P. & Seward, L. E. (2011). Applied Statistics in Business & Economics. (3rd ed.). [Vital Source digital version]. New York, New York: McGraw-Hill/Irwin.
SUO-Online Lecture. (2013). Hypothesis Testing of a Sample. Retrieved on July 2, 2013 from https://myeclassonline.com