Statistical analysis

Statistical analysis

The topic of interest– Monthly earnings of Australian people

This topic of interest is suitable to examine the available statistics regarding the populations as the monthly income of the Australian people can be measured.

Collection of the data on a population sample:

As a sample, 50 Australian people are selected that are working in different sectors and asked their monthly income for hypothesis testing. The below table is representing income of 50 Australian people that is collected from a survey:

Conducting a hypothesis test:

For defining the similarity and significance of the population, a hypothesis test can be conducted for the average income of the Australian people. In this, it is compared that the sample mean is equal to the population mean, or it is higher than population income.

H0: μ = 6,500

H1: μ >6500.

For supporting this hypothesis, the average income of the selected sample is calculated. Where M= 6,667.5 and

The hypothesis or estimated mean value = 6500

In order to test this hypothesis test, z test would be conducted as the sample size is not larger than 50 (n>50). The formula for z test statistic is calculated as below:

= (6,667.50-6500) / (2132.56 / √50)

=167.5 / 304.635

= .5498

Support of findings:

The above test is showing that the ‘z’ score of the hypothesis is 0.5498. On the basis of the positive z table, the value of this hypostasis will be equals to 0.7088. However, based on the above results, it can be said that the claimed mean no far away from the selected sample regarding standard error as it is a nearby one. As a result, it can be said that 6,667.50 is greater than 6500, but it is not much higher. It has corresponded with the probability where it is found that Z is greater than 6500 (z > 6500), so that Z value is 0.7088.

Several recent articles have supported that the annual average salary in Australia is approx $72,000 to $94,000 in different geographical areas. It is dominating that the monthly salary of an individual is $6000 to $7800. According to the Australian Bureau of Statistics, the average weekly ordinary time earnings of Australian adult is $1,634, and the monthly earning is also nearby $6,500 to $8,000 (ABS, 2019). It is supportive of our hypothesis analysis, where we estimated that the monthly salary of Australians is $6,500.

In concern to this analysis, it can be said that the sample does not have any different characteristics. Any characteristic might impact on the results of the hypothesis, including social, economic, geographical, and cultural. The variables also might have differences with the income of the population and different eras.

Conclusion and recommendation

Based on the above analysis, it can be said that there is much low possibility of Type I error because this error rejects the null hypothesis. But in concern to Type II error, it can be said that it has a higher possibility. In this concern, it can be said that the average monthly income of the Australian people will be more than $6500. Based on the above analysis or results, it could be suggested to business organizations that an organization has to provide approx $6500 as a monthly wage or salary when it stars the business in Australia