Week 6 Assignments

Introduction

In this project I selected six variables from the ' SampleDataSet.xlsx'. Among these six variables three of them were continuous and the reaming three were discrete variables. The continuous variables selected for this study are Age, WealthScore and MedianSchoolYears. The discrete variables selected for this study are NumberOfChildren, MailResponder and NumberOfCars.

Analysis

Age

The age is a continuous variable which takes only positive values even though we usually consider the integer part of it. The descriptive statistics summary of the age variable are shown below.

Table -1: Descriptive statistics of Age

Table-1, shows that the data consists of the ages of 2000 people. The mean age is 46.202 years, median age is 48, but the mode is 0. The largest age is 96 with variability measured by standard deviation is 20.85.

Graph-1: Distribution of Age

The age distribution using histogram is shown is Graph-1. Bearing a clustering at 0, the distribution of age is approximately symmetric.

Wealth Score

Table -2: Descriptive statistics of WealthScore

Table-2, shows that the data consists of the wealth scores of 2000 samples. The mean score is 301.84, median age is 299.01 and the mode is 490.46. The largest age is 490.46 with variability measured by standard deviation is 94.35.

Graph-2: Histogram of wealth score

The histogram of the wealth scores in Graph -2 shows that the distribution is approximately symmetric and bell shape.

Median School years

Table -3: Descriptive statistics of MedianSchoolYears

From Table-3 we can see that the sample consists of the median school years of 1903 people. The mean of the variable is 13.26 years, median age is 13.2 and the mode is 12 years. The maximum years is 18.1 with variability measured by standard deviation is 1.42 years.

Graph-3: Histogram of school years

The histogram of the median school years in Graph -3 shows that, the distribution is approximately positively skewed.

Number of Children

Table -4: Descriptive statistics of the number of children

The descriptive statistics of the number of children shows that the average number of children is 0.586 with majority having no children. Further the distribution of the number of children is positively skewed.

Table -4: Frequency table representing the number of children

Graph-4: Frequency distribution of the number of children

Graph-5: Pie chart representing the number of children

Mail Responder

The mode of the variable mail responder is 2

Table 5: Frequency of the mail responder

Graph-6: Pie chart representing the mail responder

It shows that the mode of the variable mail responder is 2.

Number of cars

Table 6: Descriptive statistics for the number of cars

Hypothesis tests

The first hypothesis tested in this study is regarding the mean age. The null hypothesis H0 was that the mean age of the population is 50. Alternative hypothesis H1 was that the mean age of the population is less than 50. 5% level of significance is used to test the hypothesis. The null hypothesis was rejected (t =-8.145, df= 1999, p value <0.000) at 5% level. Therefore, we conclude that there is enough evidence to support the claim that the mean age is less than 50.

Table 7: Test for the mean age

Now the hypothesis tested in this study is regarding the mean wealth score. The null hypothesis H0 was that the mean wealth score of the population is 300. Alternative hypothesis H1 was that the mean wealth score of the population is not equal to 300. The null hypothesis was not able to rejected (t 0.871003, df= 1999, p value = 0.389) at 5% level. Therefore, we conclude that there is not enough evidence to support the claim that the mean wealth score is different from 300. Details are given in Table -8

Table 8: Test for the mean wealth score

The third hypothesis tested in this study is regarding the mean value of the median school years. The null hypothesis H0 was that the mean school year of the population is 12 years. Alternative hypothesis H1 was that the mean school year of the population is greater than 12 years. The null hypothesis was rejected (t =38.672, df= 1902, p value <0.000) at 5% level. Therefore, we conclude that there is enough evidence to support the claim that the mean of teh median school years is greater than 12.

Table 9: Test for the mean school years

Now a chi-square test is conducted to test the independence of the number of children and the number of Cars. The null hypothesis H0 was the number of children and the number of cars is independent. The alternative hypothesis H1 is that the number of children and the number of cars is dependent

Table 10: Contingency table

Table 11: Hypothesis test

The null hypothesis was not to reject ( = 35.99, df=36, p value <0.4961 ) at 5% level. There is not enough evidence that the number of children is independent of the vehicles.

Limitations of the study

There were a number of missing observations in the variable, number of cars. The t test assumes that the distribution of the population is normal. But we have not conducted the study for normality of the populations.

References

Doane and Seward (2010), Applied Statistics in Business and Economics: the McGraw Hills Ltd.

Linda, Marchal, and Wathen (2008), Statistical Techniques in Business & Economics, 13th

edition. New York, NY: McGraw Hill.

Number of Children

Number of childrens

Histogram of Age

Age

Frequency

Distribution of WealthScore

WealthScore

Frequency

Histogram of MedianSchoolYears

MedianSchoolYears

Frequency