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Non Parametric Test Sample Assignment

Questions: Test the hypothesis of no difference between the ages of male and female employees of a certain company using Mann-Whitney U test for the sample data. Use the 0.10 level of significance.
Males    :    31    25    38    33    42    40    44    26    43    35
Females:    44    30    34    47    35    32    35    47    48    34

Solutions:
Age        Rank        Age            Rank            Rank of Males
25        ___1_        35__            10 _______           4
26        ___2_        38__            12_______            1
30        ___3_       40___           13______            12
31        ___4_       42 ___           14 _______          6
32       ___ 5_       43___            15______            14
33       ___ 6_       44___            16.5 _____          13
34        ___7.5_    44___            17.5 ____           16.5
34       ___ 7.5_    47___            18.5 _____           2
35        ___10       47 ___           18.5_____           15
35       ___ 10       48___            20______            10
                                        ___________________93.5

Here n₁ = 10, n₂ = 10 (samples sizes need not be same)
Sum of ranks R₁ = 93.5
U – statistics, U = 1112 + n₁(n₁ + ₁)  - R₁
                2
= 10 x 10 + 10 x 11 – 93.5
        _______2
= 100 + 55 – 93.5 = 61.5

H₀ = n1 + n2 observations cam from identical population U.

U = n₁n₂ = 10 x 10 = 50
    __2_____    2


Testing the hypothesis:
H₀ → μ₁ ≠ μ₂ i.e. there is no difference between the two populations and hence the same mean.
H₁ → μ₁ ≠ μ₂ i.e. there is a difference between the two populations i.e.,  they have different means.

α = level of significance for testing H0 and H1


Now for a two-tailed test at 0.1 level, we would accept the hypothesis H₀ if -1.64 < z > 1.64 and here z = 0.87, we conclude that the mean ages are not significantly different i.e., null hypothesis is accepted at 0.1% level.

Other Sample Assignments in Statistics Homework Assignment :

Continious Distribution	Descrete Distributions
Descriptive Statistics	Nonparamatric Statistics
Probability	Sampling And Sampling Distribution
Statistical Inference Estimation For Single Popula	Simple Regression Analysis
Statistical Inference About 2 Population	Time Series Forcasting Index Number
Statistical Quality Control	Correlation
Index Number	Larger Sample Mean Proportions
Non Parametric Test	Probability Theory
Sampling Distribution	Simple and Multiple Linear Regression Analysis
Unvariate Analysis

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