Data Analysis Assignment: Statistical Tests and Hypothesis Testing

This document presents a comprehensive solution to a data analysis assignment. The solution includes detailed calculations for Z-values, p-values, and the assessment of expectation and variance. It covers the computation of Z values, determining whether p(X > 4), and assessing expectation and variance X. The solution proceeds to calculate the mean and standard deviation, followed by an analysis involving degrees of freedom and critical F values. Finally, the assignment addresses hypothesis testing, specifically exploring the independence of gender and voting preferences. This involves stating null and alternative hypotheses, finding the statistic value, assessing the critical value, and explaining the decision-making process based on a p-value comparison, ultimately proving the alternative hypothesis.

DATA ANALYSIS

TABLE OF CONTENTS
QUESTION 1..................................................................................................................................1
a....................................................................................................................................................1
b. Determining whether p (X > 4)...............................................................................................1
c. Assessing expectation and variance X.....................................................................................1
QUESTION 2..................................................................................................................................1
QUESTION 3..................................................................................................................................1
QUESTION 4..................................................................................................................................2
Finding statistic value..................................................................................................................2
Assessing critical value................................................................................................................3
Explaining decision and interpreting results................................................................................3
P value is below the level of 0.05 so alternative hypothesis is proved........................................3

QUESTION 1
A.
Computation of Z value from P
Particulars Figures
P value or probability 0.8
Z value 0.84162
B.Determining whether p (X > 4)
0.41
C. Assessing expectation and variance X
0.034
QUESTION 2
Mean - μ / Standard deviation
Particulars Figures
Mean 0.51
μ 0.50
Standard deviation .04
Mean - μ / Standard deviation 0.51 - 0.50 / .04
= .25
QUESTION 3
Particulars Figures
Degrees of freedom 1 2
Degrees of freedom 2 12
Probability or confidence level 0.05
Critical f value = Between group variability
/ within-group variability
3.88
1

(value is derived by seen f statistic table
when p = 0.05)
QUESTION 4
Stating null hypothesis
Null hypothesis (H0): Gender and voting preferences are independent.
Alternative hypothesis (H1): Gender and voting preferences are not independent.
Finding statistic value
DF = (r - 1) * (c - 1)
= (2 - 1) * (3 - 1)
= 2
Particulars Outcome
E1,1 (400 * 450) / 1000
= 180000/1000
= 180
E1,2 (400 * 450) / 1000
= 180000/1000
= 180
E1,3 (400 * 100) / 1000
= 40000/1000
= 40
E2,1 (600 * 450) / 1000
= 270000/1000
2

= 270
E2,2 (600 * 450) / 1000
= 270000/1000
= 270
E2,3 (600 * 100) / 1000
= 60000/1000
= 60
Particulars Outcome
Χ2 = Σ [ (Or,c - Er,c)2 / Er,c ]
Χ2 (200 - 180)2/180 + (150 - 180)2/180 + (50 -
40)2/40 + (250 - 270)2/270 + (300 - 270)2/270 +
(50 - 60)2/60
Χ2 400/180 + 900/180 + 100/40 + 400/270 +
900/270 + 100/60
Χ2 2.22 + 5.00 + 2.50 + 1.48 + 3.33 + 1.67 = 16.2
Assessing critical value
P(Χ2> 16.2) = 0.0003
Explaining decision and interpreting results
P value is below the level of 0.05 so, alternative hypothesis is proved.
3