BUS5SBF Statistics For Business and Finance Assignment

Organise your sample data in a spreadsheet as per the instructions in the Excel sheet

a. What sampling method is used to select your sample data?
b. Do you think that is the best method of sampling? Why not? Why yes?
b. What is the best statistic used to compare the volatility in WEF, WI, and FS values? Why?

Answer:

The data has been organized as per the instruction and is found in sheet one of the excel document.

A probability sampling method known as simple random sampling also known as equal chance method (John, 2009) & (Saunders & Thornhill, 2012) has been used to select the sample data.

Simple random sampling is an appropriate method of sampling since it always eliminates biasness (Gravetter , 2011).

Sometimes choosing the right test statistics to compare samples is so challenging especially to individuals who are not well grounded in the field of statistics(Golafshani, 2003). However, there are several ways of choosing a test statistic that is appropriate for a given data. First of all we know whether the data is nominal, ordinal or ratio (Utts, 2014). We should also know the number of samples that are there and whether they are paired or unpaired (David & George , 2006). For this kind of data, the best test statistics to use in comparing the volatility of the three variables (WEF, WI, FI) is one way analysis of variance (ANOVA) since the variables are more than two (Peace & Parrillo, 2008).

All the workings of this task are as done on the excel sheet two on the attached excel document.

According to the income distribution plotted in the excel sheet, it is evident that the most frequent group is the group. This because compared to other groups, it has the highest number of low income earners. Statistically, this shows that the data is skewed to the left. It has got a long tail towards the right side. From the descriptive statistics summary in the excel sheet, it is observed that the skewness value is 2.56. For a normal skewness, the value should be zero. This also indicates the data is positively skewed.

The data is not normally distributed even from the look of the graph drawn. This is because the data contains very few people of high income and very many people earning low income. A normally distributed income would have consisted of few high income earners, relatively more high income earners and few low income earners so that the graph assumes a bell-shape. The following descriptive table explains more about the distribution.

Descriptive statistics table

Column1
Mean	441.75
Standard Error	29.47917044
Median	362.5
Mode	210
Standard Deviation	294.7917044
Sample Variance	86902.14899
Kurtosis	8.908273487
Skewness	2.559223142
Range	1900
Minimum	106
Maximum	2006
Sum	44175
Count	100

Table 1.

For a normally distributed data, the mean, mode and median are usually the same. In this WI data, the three measures are different. Mean = 441.75, median = 362.5 and mode = 210. This means that the data is not normally distributed.

Top 10% value is also known as the 90^th In determining percentiles, the data is always divided into 100 equal portions so that we have 1^st percentile to 100^th percentile. It has been calculated in the excel sheet using the formula, =PERCENTILE.EXEC(RANGE,K) where k denotes the corresponding percentile that is being determined. Note that the data must first be arranged from the smallest value to the largest value using the sort and filter facility. In this question, the top 10^th value in WEF is, 191.3. The bottom 10% value is known 10^th percentile and is also calculated using the same procedure. From the excel sheet, the answer is 36.

The question is not clear at the end.

Chances that family size = 2 is 0.27. The total number of families in this economic data was 100. Out of these 100 families, 27 have a family size of two people. This means that the chances of a family having two people in this area is 27 expressed as a fraction of 100.

The WEF sample data has got two outliers. This has been determined with the use of a scatterplot as shown in sheet 3. The appropriate way to measure the extent of dispersion in WEF data is by applying the use of box plot which also measures normality of a set of data.

The chances that the head of a household is a woman and has primary education = 0.105

The chances that the head of a household is a man and has college degree = 0.0195

The fraction of males with secondary education = 0.754

The fraction of males with secondary education = 0.046

The two events are independent as each of them does not affect the occurrence of the other. In other words, gender of household head does not influence in any way having a college degree.

References

David, S., & George , P. (2006). Introduction to the practice of Statistics. Freeman.

Dawson , B., & Trapp, G. R. (2001). Basic clinical Biostatistics. New York.

Golafshani, N. (2003). Understanding reliability and validity of qualitative research.

Gravetter , F. J. (2011). Research methods for behavioral sciences.

John, H. (2009). Statistics Glossary.

Notz, W. I. (2012). Statistics Concepts.

Peace, K. E., & Parrillo, A. V. (2008). Assessing the validity of statistical inferences in public health research.

Saunders, M., & Thornhill, A. (2012). Research methods for business students. Pearson Education.

Utts, J. M. (2014). Seeing through Statistics.

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