1. New Information Technologies in Learning Statistics M. Mihova, Ž. Popeska Institute of Informatics Faculty of Natural Sciences and Mathematics, Macedonia marija@ii.edu.mk, zaneta@ii.edu.mk marija@ii.edu.mk, zaneta@ii.edu.mk

2. About the course Course in the sixth semester Course in the sixth semester –two hours of lecture –two hours of theoretical exercises –one hour of laboratory exercises per week

3. Topics: Descriptive statistics, Descriptive statistics, Sampling Distributions, Sampling Distributions, Estimation, Estimation, Test of Hypothesis, Test of Hypothesis, Nonparametric Tests and Categorical Data Testing, Nonparametric Tests and Categorical Data Testing, Linear Regression, Linear Regression, Analyses of variance (ANOVA). Analyses of variance (ANOVA).

4. Lecture and theoretical exercise Theory of mathematical statistics Theory of mathematical statistics Examples of application of the theory in the field of informatics and other fields Examples of application of the theory in the field of informatics and other fields

5. LABARATORY EXERCISE demonstrations with statistical applets, demonstrations with statistical applets, exercise using statistical package exercise using statistical package made programs for some statistical methods made programs for some statistical methods

6. Applet for demonstration central limit theorem

7. Applet for plotting density functions for distributions Demonstration that t- distribution with higher degrees of freedom is closer to the normal N(0,1). Demonstration that t- distribution with higher degrees of freedom is closer to the normal N(0,1).

8. Statistical packages SPSS SPSS –Organizing data set

9. Statistical packages Analyzing data set Analyzing data set

10. Programming statistical methods Statistical packages are useful only for well known distributions. Statistical packages are useful only for well known distributions. Mathematica Mathematica Programs for estimating parameters by method of moments, testing parametric and nonparametric hypothesis, finding confidence intervals… Programs for estimating parameters by method of moments, testing parametric and nonparametric hypothesis, finding confidence intervals…

11. Example a0=Input[“Inpit 0”]; X=Input[“Input Data”]; n=Length[X]; z=Input[“Input significant level”]; k1=FindRoot[Integrate[x^(n-1)*E^(-x)/(n-1)!,x]==z, {k,20}][[1]][[2]]; Print[“k1*a0=”, k1*a0]; s=Sum[X[[i]],{I,1,n}]; Print[“s=”, s]; If[s>k1*a0, Print[“hypothesis is accepted”], Print[“hypothesis is not accepted”]]; For data set X={0, 1.1, 3. 4.4, 4.9, 5, 5}, 0=5 and  =0.05 the output is: k1*a0=16.4266, k1*a0=16.4266,s=23.4 “hypothesis is not accepted”

12. Thanks for your attention