Public University of Navarre

CastellanoEuskara | Academic year: 2018/2019 | Previous academic years:  2019/2020  |  2017/2018  |  2016/2017  |  2015/2016 
Bachelor's degree in Innovation on Food Processes and Products at the Universidad Pública de Navarra
Course code: 502203 Subject title: STATISTICS
Credits: 6 Type of subject: Basic Year: 1 Period: 2º S
Department: Estadística, Informática y Matemáticas

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Module/Subject matter




Descriptive statistics, probability, statistical inference


General proficiencies


CB1: Students have demonstrated that they possess knowledge of and understand an area of study, based on general secondary education and usually at a level which, albeit with the support of advanced text books, also includes some aspects which imply knowledge of the latest developments in their field of study.


CB2: Students know how to apply their knowledge to their work or vocation in a professional manner and possess skills which are usually demonstrated by developing and defending arguments and resolving problems in their area of study.


CB3: Students are able to compile and interpret relevant information (normally within their area of study) in order to voice opinions which include reflection on relevant themes of a social, scientific or ethical nature.


CT3: The ability to manage information. To identify information needs and be familiar with the sources, bibliographical resources and services available in order to perform basic research in the field of study. To classify information according to relevancy and analyse it critically.


CT4: A capacity for team work. To define the group¿s objectives, rules of operation and work plan. To participate actively and in a balanced manner in team work, sharing information and results. To plan the agenda of activities and meetings, reviewing the group¿s progress and task integration. Conflict resolution and negotiation. To evaluate the group¿s effectiveness in terms of results achieved.

CT5: Ability of self-learning

CT6: Ability of solving new problems and decision-making capability



Specific proficiencies

CE1. Conocer los fundamentos de Ciencias Básicas (matemáticas, física, química, biología, bioquímica) que le permitan resolver los problemas técnicos relacionados
con Tecnología de Alimentos.
CE2. Ser capaz de utilizar sistemas operativos, bases de datos y programas informáticos en la resolución de problemas relacionados con la industria alimentaria y el
desarrollo de nuevos productos y procesos alimentarios. Utilización de sistemas integrados de gestión empresarial (ERP) para la optimización de procesos en la
empresa alimentaria.


Learning outcomes

R1.- To carry out statistical analysis of data to summarize a report in an efficient and accurate way

R2.- To know a statistical package for working with data bases and simulation of random experiments

R3.- To model problems of random properties using probabilities, conditional probabilities and independent events

R4.- To recognize the main discrete and continuous probability distributions, and the main rules of probabilities

R5. Utilizar las técnicas inferenciales clásicas:estimación puntual, por intervalos y contrastes de hipótesis.


R6.- To know basic statistical models used in design of experiments,  assessment and environmental problems




Methodology - Activity Attendance  Self-study
A-1 Theoretical clases 44  
A-2 Computer Labs 14  
A-3 Debates, group work, etc 1  
A-4 Monitoring proofs 8  
A-5 Lecture    
A-6 Self-study    75
A-7 Exam, evalutaion proofs 4  
A-8 Tutorial 4  
Total 75 75


Relationship between formative activities and proficiencies

Proficiency Activities
CT3-CT6 A-1, A-2, A-3
CB1-CB3 A-1, A-2, A-4, A-6, A-7
CE1, CE2 A-1, A-2, A-3, A-4, A-6,A-7








 Learning Outcomes Evaluation Activity Weight (%)  Second chance
  R1-R2-R3-R4-R5-R6  Exam of theory and practice with computer  60  Yes
  R1-R2-R3-R4-R5-R6  Parcial Exam  30 No
  R1-R2-R3-R4-R5-R6  Monitoring Proof  10 No






Descriptive Statistics


  • Exploring Data



  • Sampling space and events
  • Condicional probability, the law of total probability, Bayes theorem and independent events
  • Probability density function and cummulative density function. Median, mode, percentiles and moments
  • Discrete random variables: Uniform, binomial and Poisson. Continuos random variables: Uniform, exponential, gamma and normal
  • Joint, marginal and conditional distributions of discrete and continuous random variables


Inferencial Statistics


  • Itroduction to sampling distributions. Parameters and estimators.
  • Chi-square distribution and t-Student
  • Sampling distribution of the mean, of the difference of means, proportion, difference of proportions
  • F Distribution
  • Sampling distribution of the variance and of the ratio of variances
  • Point Estimation and properties. Mean squared error
  • Confidence intervals introduction. Confidence intervals of means, difference of means, proportions, difference of proportions, variances and ratio of variances
  • Hypothesis testing. Type I and type II errors. P-value and power of a test.  Hyphotesis testing for means, proportions and variances

 Statistical Modelling


  • Analysis of variance and Regression






Week 1: Descriptive Statistics

Weeks 2-5: Probability 

Weeks 6-15: Inferencial Statistics






Acceda a la bibliografía que su profesor ha solicitado a la Biblioteca.



Ugarte, M. D., Militino, A. F., Arnholt, A. T. (2016). Probability and Statistics with R.  2nd Edition. CRC Press/Chapman and Hall.




Devore, J. (2005) Applied statistics for engineers and scientists. Thomson

Montgomery, D.C. (2002). Probabilidad y Estadística aplicadas a la ingeniería. Limusa-Wiley





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