Statistics for Dummies Workshop **You’re not really Dummies**

Before Starting Disclaimer: We can’t teach a whole quarter of statistics, but we can teach you how to study. Studying for statistics requires reading the book! If you are not reading on your own and just taking notes in class, you are likely not to succeed Upper Level classes will automatically assume you have learned to study the material DO NOT Chegg or Google the solutions

What’s going to be covered Diagrams Data Summary and Presentation Binomial distribution Engineering/Statistics Toolbox Z-test Type 2 Error T-test  2 Test

Box Plot Dot Diagram Q1Q1 Q2Q2 Q3Q3 IQR 1.5 IQR IQR = Inter Quartile Range x = 1550

Histogram

Data Summary Correlation Coefficient Stem and Leaf Diagram Quartile/Percentile Calculation R =  n i = 1 (x i – x)(y i – y)  n i = 1 (x i – x) 2  n i = 1 (y i – y) 2 Stem Leaf Freq ( )( ) QuartilePercentile (n + 1) 1 st 2 nd 3 rd 2(n + 1) 3(n + 1) th 95 th.05(n + 1).95(n + 1) Value will give ordered observation Interpolate as needed

Binomial Distribution ( ) P(X = x) = nxnx p x (1-p) n-x ( ) nxnx = n! x!(n – x)! We use Binomial Distribution when: 1.Trials are independent 2.Each trial results in one of two possible outcomes, success or failure ooooh! 3.The probability, p, remains constant

Engineering/Statistics Toolbox Known as the procedure for hypothesis testing Steps for Generic Hypothesis Testing 1. Identify Parameter Of Interest: For instance; determine the saltiness of a potato chips 2. State the Null Hypothesis (H 0 ): Standard that you are testing against, like the given average students test scores 3. Alternative Hypothesis (H 1 ): Specify an appropriate alternative hypothesis 4. Test Statistic Equation you are going to use for each test. Z = X-  /(  /n^.5) 6. Computations Plug and chug 7. Conclusion Decide whether the Null Hypothesis should be rejected and report and that in the problem context.

Z-Test When do you use it? Known mean and known variance Gives the probability density of when something is going to happen Most of the time an alpha value will be given to you If not, assume 0.05

Type II Error When you fail to reject the null hypothesis when it is wrong then you have committed a type II error  =  Z 0 ) Power = 1 -  For instance: Say you have a pop. of 50 beads with an average diameter of 10 mm (actual average diameter). However, your sample of 10 beads has an average of 15 mm. You want to confirm that a null hypothesis of 15 inches is correct. If you fail to reject the null you messed up.

T-Test Unknown variance and known mean You need to determine the sample variance You need to know degrees of freedom That will be n-1, (n is the sample size) Literally the same as the Z-test except with degrees of freedom and sample variance

 2 -Test This is a test on the sample variance Much the same as T-test Must know the sample variance, as well as the actual variance This tests variance, NOT standard deviation