Statistical Analysis Of Estimated Resident Population Number In Australia In 2015

Research Hypotheses

The use of statistical analysis for the collected data is very important for effective decision making. Here, we want to collect the data regarding the biological phenomenon and then analyze this data. Here, we have to collect the data for the male and female estimated resident population number for the year 2015 and then we have to analyse this data by using different statistical tools and techniques. We have to use descriptive statistics, graphical analysis, and inferential statistics or testing of hypothesis for this research project. We will use different statistical tests for checking the research hypotheses for this research project. Let us see this research study in detail explained in the next topics.

For this research study, the research hypotheses or claims are established as below:

Null hypothesis: H₀: There is no any significant difference in the average number of estimated resident population for the given four age groups in the year 2015.

Alternative hypothesis: H_a: There is a significant difference in the average number of estimated resident population for the given four age groups in the year 2015.

Null hypothesis: H₀: There is no any statistically significant difference in the average male estimated resident population number and average female estimated resident population number for the year 2015.

Alternative hypothesis: H_a: There is a statistically significant difference in the average male estimated resident population number and average female estimated resident population number for the year 2015. 

Data for this research project is collected from the social health atlas of Australia. This is the data by local government area published on May 2017. This data includes the population characteristics such as demography, socio-economic status, health status and risk factors, and use of health and welfare services. The sample data for the male and female for the estimated resident population number is selected for this research project. Also, the data for four different age groups of males for the estimated resident population number is selected for checking the significant difference. The complete data is given in the separate excel sheet.      

In this section we have to analyze the collected data by using the statistical tools and techniques. We have to use the descriptive statistics and inferential statistics for the analysis of given data. We get the general idea about the nature and spread of the variable by using the descriptive statistics. Also, we have to use inferential statistics or testing of hypothesis for checking the hypotheses or claims established for this research project.

First of all we have to check the claim or research hypothesis whether the average number of estimated resident population for the given four age groups in the year 2015 are same or not. For checking this claim or hypothesis we have to use the one way analysis of variance or single factor ANOVA. We assume the level of significance for this test as 5%. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H₀: There is no any significant difference in the average number of estimated resident population for the given four age groups in the year 2015.

Data Collection

Alternative hypothesis: H_a: There is a significant difference in the average number of estimated resident population for the given four age groups in the year 2015.

The required descriptive statistics and ANOVA table is summarised as below: 

ANOVA: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Male 0 to 4 years ERP Number	30	59554	1985.13	9323051.36
Male 5 to 9 years ERP Number	30	57022	1900.73	8425044.48
Male 10 to 14 years ERP Number	30	51762	1725.40	6747511.14
Male 15 to 19 years ERP Number	30	53959	1798.63	6983603.55
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1169222.42	3	389740.81	0.05	0.99	2.68
Within Groups	912897105.50	116	7869802.63
Total	914066327.92	119
			Level of significance	0.05

For this test, the test statistic value is given as F = 0.05 with p-value as 0.99.

Here, P-value > α = 0.05

So, we do not reject the null hypothesis at 5% level of significance

We do not reject the null hypothesis that there is no any significant difference in the average number of estimated resident population for the given four age groups in the year 2015.

There is insufficient evidence that there is a significant difference in the average number of estimated resident population for the given four age groups in the year 2015.

Now, we have to see the descriptive statistics for the two variables such as male estimated resident population number and female estimated resident population number.

The average male estimated resident population number is given as 1855 approximately with the standard deviation of 2636.88 while the average female estimated resident population number is given as 1963 approximately with the standard deviation of 2813.34. The minimum male estimated resident population number is observed as 49 while the maximum male estimated resident population number is observed as 11884. The minimum female estimated resident population number is observed as 56 while the maximum estimated resident population number is observed as 12686. Data for the male estimated resident population number is very highly skewed at positive side or right skewed. Also, data for the female estimated resident population number is very highly skewed at right side.

Now we have to check other hypothesis or claim whether the average male estimated resident population number is same as the average female estimated resident population number or not. For checking this hypothesis or claim we have to use 5% level of significance. For this hypothesis, we have to use the two sample t test for the population mean assuming equal variances. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H₀: There is no any statistically significant difference in the average male estimated resident population number and average female estimated resident population number for the year 2015.

Alternative hypothesis: H_a: There is a statistically significant difference in the average male estimated resident population number and average female estimated resident population number for the year 2015.

This is a two tailed test.

The test statistic formula for this test is given as below:

Test statistic = t = (X1bar – X2bar) / sqrt[((S1^2/N1)+(S2^2/N2)]

The excel output for this test is given as below:

t-Test: Two-Sample Assuming Equal Variances
	Male ERP number	Female ERP Number
Mean	1855.033333	1963.266667
Variance	6953126.861	7914882.547
Observations	30	30
Pooled Variance	7434004.704
Hypothesized Mean Difference	0
df	58
t Stat	-0.153742963
P(T<=t) one-tail	0.439173048
t Critical one-tail	1.671552763
P(T<=t) two-tail	0.878346097
t Critical two-tail	2.001717468

For this test, we get the p-value as 0.8783 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis at 5% level of significance. We do not reject the null hypothesis that there is no any statistically significant difference in the average male estimated resident population number and average female estimated resident population number for the year 2015. There is sufficient evidence that average male estimated resident population number and average female estimated resident population number are same for the year 2015.There is insufficient evidence that there is a statistically significant difference in the average male estimated resident population number and average female estimated resident population number for the year 2015.

Statistical Analysis

Situation: Most of the time it is observed that the average number of estimated resident population for different age groups within male and female are same. The same situation is observed for the given four age groups. The average number of estimated resident population for different age groups founds to be approximately equal. Also, the concept is same for the male and female. The average number of estimated resident population for male and female is same.

Task: For this research study, we mainly conduct two tasks by using the testing of hypothesis. In the both task we have to find out the significant differences in the estimated resident population number. For the first situation we have o analyze it for different age groups of males and then we have to analyze it for male and female. We want to check this situation by using the four different age groups of the male population. We consider the primary four age groups for checking this fact. The four age groups of male persons are selected. The primary age groups are selected for this analysis. The four age groups include the groups such as 0 to 4 years, 5 to 9 years, 10 to 14 years and 15 to 19 years. Also, we want to check statistically significant difference in the average male estimated resident population number and average female estimated resident population number for the year 2015.

Action: Here, we want to compare the more than two population means. For checking this fact or claim whether there is any significant difference in the average number of estimated resident population for different age groups, we need to use the one way analysis of variance or single factor ANOVA test and we used this test for checking this hypothesis. For the given ANOVA test, we do not reject the null hypothesis that there is no any significant difference in the average number of estimated resident population for the given four age groups in the year 2015. There is insufficient evidence that there is a significant difference in the average number of estimated resident population for the given four age groups in the year 2015. From the given statistical analysis, it is found that there is sufficient evidence that average male estimated resident population number and average female estimated resident population number are same for the year 2015.

Result: For this hypothesis, we concluded that there is insufficient evidence of significant difference in the average number of estimated resident population for different age groups. Also, there is sufficient evidence that average male estimated resident population number and average female estimated resident population number are same for the year 2015.

Conclusions

The average male estimated resident population number is given as 1855 approximately with the standard deviation of 2636.88 while the average female estimated resident population number is given as 1963 approximately with the standard deviation of 2813.34.

There is insufficient evidence that there is a significant difference in the average number of estimated resident population for the given four age groups in the year 2015.

There is sufficient evidence that average male estimated resident population number and average female estimated resident population number are same for the year 2015. 

References

Dobson, A. J. (2001). An introduction to generalized linear models. Chapman and Hall Ltd.

Evans, M. (2004). Probability and Statistics: The Science of Uncertainty. Freeman and Company.

Hastle, T., Tibshirani, R. and Friedman, J. H. (2001). The elements of statistical learning: data mining, inference, and prediction: with 200 full-color illustrations. Springer – Verlag Inc.

Hogg, R., Craig, A., and McKean, J. (2004).  An Introduction to Mathematical Statistics. Prentice Hall.

Liese, F. and Miescke, K. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer.

Pearl, J. (2000). Casuality: models, reasoning, and inference. Cambridge University Press.

Ross, S. (2014). Introduction to Probability and Statistics for Engineers and Scientists. London: Academic Press.

Todd, G. (2007). Descriptive Statistics. Topics in Biostatistics. New York: Springer.