Probability & statistics

Analysis of First data
It include the height and weight of adults and data is taken from the cite
http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_Dinov_020108_HeightsWeights
Q.1    Calculate the mean, standard deviation and Quartiles
Ans.    This is the table of Statistics which is obtained by SPSS, include mean, standard deviation and quartiles Q1, Q2, Q3.
    Statistics
    
    
    Height
    Weight
    N
    Valid
    200
    200
    
    Missing
    0
    0
    Mean
    67.9498
    1.2722E2
    Std. Deviation
    1.94036
    1.19610E1
    Percentiles
    Q1 25
    66.5075
    1.1988E2
    
    Q2 50
    67.9350
    1.2788E2
    
    Q3 75
    69.2075
    1.3617E2
Q.2    Apply Chi-square distribution for this data set.
Ans.    Firstly we classify the data into categories low, medium and high. Categories are chosen as,
In case of height, low = 63 to 66, medium = 66 to 69 and high = 69+
In case of weight, low = 97 to 117, medium = 117 to 137 and high = 137+
Now we apply the chi-square distribution to test the independence of attributes.
Null hypothesis: Height and Weight are independent to each other.
Alternative Hypothesis: Height and Weight are independent to each other.
Level of significance: 5%
Cross table and chi square table of SPSS are given below:
    Height * Weight Crosstabulation
    Count
    
    
    
    
    
    
    
    Weight
    Total
    
    
    high
    low
    medium
    
    Height
    high
    24
    5
    28
    57
    
    low
    0
    20
    16
    36
    
    medium
    19
    19
    69
    107
    Total
    43
    44
    113
    200
    Chi-Square...