2-Sample T-test for Means What is mu? Steps to the Test Categorical vs. Quantitative By: Laura Hasley Statistics Gr.12

What is Mu? Mu is the symbol used when talking about a population mean or average. For all of the significance tests involving means, the parameter being studied is mu. Since you can’t test mu because it’s unrealistic to think you can test the whole population, you would take a sample of the population. With that sample, the sample mean is calculated and called x-bar. Just like from the proportion tests, mu is to x-bar as p is to p-hat. So, by analyzing x-bar and coming up with a conclusion for the probability value, you can asses the validity of the statements about mu.

2-Sample T-Test for Means Steps to the Test When performing a 2-sample t-test for means, the first step is to name the test. After that, you must define the parameter that is being studied. For this type of test there would be two population means to define. Next, you have to state the null hypothesis and the alternative hypothesis. We will test that the sample average for data set A is greater than the sample average from data set B. Following that, you must check the conditions. Since there are two sets of data, you have to make sure both sets meet the condition. The conditions are each sampled used must be a random sample and the sample sizes must be greater than thirty. After that, state the significance level. This will always be provided in the given information. Next, you are to sketch the distribution. Calculate the first sample mean and subtract from it the second sample mean. Mark what this value is on the graph. From there shade in all of the area to the right of the mark. After the sketch, use your calculator to find the value for T and P. Based on the value found for P, make the correct conclusion for the test. You will either reject the null hypothesis or not reject it 2-Sample T-Test for Means 1. Name the Test 2. Define the parameter 3. Hypotheses 4. Conditions 5. Significance Level 6. Sample Distribution Sketch 7. T-value 8. P-value 9. Conclusion

Categorical vs. Quantitative When determining what type of inference procedure to conduct, the first thing is to determine if the data provided is categorical or quantitative. This is important because there are very different procedures to carry out depending on what type of data is given. For categorical data, the parameter studied is the population proportion while the population mean is the parameter for quantitative data. Also, the test statistic and conditions are different for each type of data. The test statistic calculated for the categorical data is Z while the quantitative data leads to calculating T. The conditions for quantitative data are that the samples must be random and the sample size has to be greater than thirty. For categorical data, the conditions are that the sample size multiplied by the p-value must be greater than ten and that the sample size multiplied by (one – the p-value) must be greater than ten. With all of this in mind, it is crucial to pick up on what kind of data is being presented. Most of the time, if the problem suggests anything about averages and means, the data is quantitative. Any talk about proportions or given percentages almost always means the data is categorical. Categorical Quantitative Parameter P Mu Test Statistic Z T Conditions RS; np>10; n(1-p)>10 RS; n>30

Citation Home button-Microsoft clip art Back arrow-Microsoft clip art Forward arrow-Microsoft clip art Mu symbol-http://openlab.citytech.cuny.edu/2013-spring-mat-1272-reitz/2013/05/16/study-guide-for-problem-3/ Clipboard checklist button-Microsoft clip art VS. symbol-http://www.dayhwstoodstill.com/2011/04/six-best-versus-films.html Works cited icon on slide one-http://www.narragansett.k12.ri.us/NHS/computer/First_Semester_09_10/FS_2009_Period_3A/Devin_Gould_Google_vs_Bing/workscited.htm Chart on slide 2- http://bolt.mph.ufl.edu/6050-6052/unit-3b/module-9/