Exercise 10 3. Distance from student residence to school (Km) and time (minute) spent for that distance by students are given in the following table: Distanc e Time Distanc e Time 11 60 3 15 25 60 6 30 3 7 2 15 15 30 2 30 2 15 3 20 6 15 7 25 10 20 5 25 3
Exercise 9 Asking people in 3 districts about housing preference we see that Ba Dinh: 450 like apartments in high buildings, 400 do not like; Dong Da: 230 like apartments in high buildings, 190 do not like; Hai Ba: 650 like apartments in high buildings, 6
Exercise 7
1. Stock prices of two companies TSM and TBS at some working days (randomly selected) are given in the following table:
Company Stock price Company Stock price Company Stock price Company Stock price Company Stock price Company Stock price TSM
Exercise 5
1. Asking 450 women and 400 men about preference of housing, the
answers show apartment favor of 300 women and 240 men. Let compare apartment preference proportions of men and women. 2. A survey on job satisfaction was done in a high school wit
Exercise 4
1. Salary of government staff depends on seniority (length of service). Then
a) What is value of correlation coefficient between salary and seniority? b) How do the correlation coefficient, mean value, median and variance of salary change (to b
Exercise 3 Data on weight and height of girl students and of their parents are given in the following table:
Observation Nr Student Weight Student Height Mother Weight Mother Height Father Weight Father Height 1 2 48 47 163 155 52 45 158 148 70 60 175 160
Sampling
Sample
Population
Estimation
Laws
Hypothesis tests
Population
How to do the sampling
- Representative for the population of study - Corresponding to study target
A. One sample model
S ampling mo de ls
One sample model usually concerns with an in
Regression Analysis
Method of Regression Analysis is used to forecast or estimate values of one variable (respond variable, predicted variable) by certain formula of one or several other variables (descriptive variables, estimators)
Example. There certain
Te s t fo r two re late d (paire d) s ample s
Co mpare two me an value s No n-parame tric te s t
Co m p are m e an v alue s o f tw o re late d s am p le s
For related variables X and Y , the comparison of mean values is equivalent to the comparison the m
Hypo the s is te s ts fo r two inde pe nde nt s ample s
Co mpare two pro po rtio ns Co mpare me an value s o f two po pulatio ns Co mpare two varianc e s
Pro ble m 3. Co m p are tw o m e an v alue s Let ( X 1 , X 2 ,., X n ) be a sample of n independent
Hypo the s is Te s t
" Hypo the s is Te s t": A procedure for deciding between two hypotheses (null hypothesis alternative hypothesis) on the basis of observations in a random sample
One s ample Hypo the s is te s t
Co mpare pro po rtio n to a g ive n va
Parameter estimation
" Es timatio n": Using lo w ac c urate measuring tools (using data collected in a ve ry limite d s ample of population) to determine as precisely as possible value of a certain parameter (of all population).
An opinion or judgment of
C. Describe relation between 2 qualitative variables Cross table with levels of one variable in rows, levels of the second variable in columns: Y(1) Y(2) X(1) n1,1 n1,2 X(2) n2,1 n2,2 X(k) nk ,1 nk ,2 K1 K2 . Y(m) n1,m n2,m nk ,m Km
M1 M2 Mk N
.
Usually,
DATA DESCRIPTION
I. PURPOSE
- Primarily describe specific characteristics of data
- Find out abnormal observations, outliers and mistakes /errors. Then clean the data before doing further analysis
- Inverstigate remarkable features of data, using those fe
What is Mathematical Statistics ?
Science of investigating population's laws
a) Population:
The set of target objects of study
- Socio-demographic study: all citizentsof a given country
Forestry survey: All trees in a study region
- Quality control: All p