International business management practices and strategies

Personal Income Probabilities

Based on this sample, and clearly showing workings, appropriate graphics and your response to blank values in the data, calculate the following:

(a) the probability of randomly picking two men over 35 from the sample

The sample consists of both men and women, however the question does not delineate segmentation by gender in regard to men vs. women, but solely requests "from the sample" the possibility of selecting men over 35 years of age each draw. Therefore the equation is:

Men over 35 years of age total in the sample.

121 participants total in the sample

239 = P of men in sample

Percentage of men over 35 in the sample 23.9%

Each draw is discreet with a 23.9% chance that a man over 35 years of age will be selected on random selection each time.

For example of work in excel: Appendix

(b) given that we are picking from men in the sample, the probability of picking a man whose job income is between £2,250 and £3,250 per month

There are 50 Men in sample making between £2,250 and £3,250 per month, or 52% (.52) of 95 men total in sample

Income distribution indicates that random draw of income between £2,250 and £3,250 would be .229

Random selection is always dependent upon the entire sample of both men and women, yet with men the designated outcome:

50/121 = .41

Random selection of a man whose job income is between £2,250 and £3,250 per month presents a 41% chance

(c) a sub-sample group of five unmarried men under 28 are to share their more detailed views of credit in a focus group. Calculate how many different ways are there of putting these groups of five together from this sample?

Sub-sample: 18 unmarried men under 28 years of age

Groups of 5 / 18 unmarried men under 28 years of age = .27777 (28%)

18 X .27777 = 4.99999986 number of groups

2 Assume that Total Income is the sum of Job Income and Additional Income.

(a) produce frequency distributions, histograms and appropriate descriptive statistics which allow a comparison of Total Income for men, with Total Income women

M= 242,916 (cumulative) (95 x 2557 avg.) W=45,665 (cumulative) (26 X1826 avg.)

Graph 1: Series 1 F/Series 2: M

Graph 2: Series 1: M / Series 2: F

(b) provide some interpretive comment on the statistical and graphical output produced, focusing both on similarities and differences between the two groups observed

Outcomes to the gender distribution of income exhibit common differences. Fewer women to the study indicate that less information is available reflective of normal population. From the convenience sample, however, there are clear differences in monthly income totals which are not inconsistent with aggregate figures in a developed national economy. The larger number of men allows for a more representative sample of a national labor index, with the bulk of the earners earning median incomes consistently, yet quite a few are also earning far more than other men in the study, as well as their female counterparts.

(c) comment on the effect that outlying data values have on the results obtained, and your consequent response to the presence of outliers in this case.

Outlier issues include zero income with potential correlation to age in instances, particularly where the smaller sample of women are concerned. This of course only impacts cumulative totals, and individual reporting is evidenced in the frequency distribution and histogram charts.

3 Assuming that the descriptive statistics for the distribution of Ages in this sample are good estimates of the parameters that apply to the background population, and that this background population is near-normally distributed, calculate the following using the z-table and/or Excel functions, clearly showing your workings:

(a) the % of the population of applicants under 35

Total population = 121

Population under 35 years of age = 79

Percent of population under 35 years of age = 65% 121/79

(b) the % of the population of applicants between 20 and 30

Total population = 121

Population between ages of 20 and 30 = 65

Percent of population of applicants between 20 and 30 = 54% 65/121

(d) the lower age limit for the oldest 10% of the population of applicants

53 years of age is the lowest limit for the oldest 10% of the applicants.

(d) how do the two answers in (a) and (b) above compare with the actual % proportions for this sample, provide explanatory comment on the differences

In regard to debt to income ratio, increase in debt to income ratio as age advances into 30s. However, in comparison with the older 10% where there is consistency in low to no debt to income ratio, a bell curve becomes evident in long-term benefits to the TOTBAL/TOTPAY as income advances and debts are paid in approach to retirement.

4 Construct 95% confidence intervals for the mean Job Income of the background population of both men granted credit, and separately for women not granted credit, (the z-table and/or the t-table and/or Excel functions can be used) clearly showing workings:

(a) Clearly state the two intervals, explaining the meaning of the figures

Formula: 95% confidence intervals indicate that the bulk of the results to analysis of a population will fall between the range of +/- -2.5% or (p - 1.96s) to +2.5% or (p + 1.96s)

Square root within the equation determines that'd = [p*(1-p)/n]

p= probability n = ratio or number

Note: request for mean in the equation indicates that the solution is an "average."

Most bell curve statistical narratives are analyzed for Median range rather than Mean.

The 95% confidence level is used to express the 'extremities' or outlier ends of the bell curve on a continuum.

Results:

Mean Job Income for men granted credit = 2866 (95% confidence interval number = +/-71.65)

Mean Job Income for women without credit = 1477 (95% confidence interval number = +/- 36.9)

(b) Provide interpretation, focusing again on differences between the two groups, paying attention to whether the two confidence intervals overlap or not The two 95% confidence intervals do not overlap due to the disparity in base income and the parameter of higher paid men with access to credit vs. The population of women with no credit, and far lower mean income not nearing the lowest interval of the men in the sample.

(c) Comment on the sample sizes here and the implication for (a), (b).

Sample size of women is too small for the study to be statistically significant in terms of knowledge of mean income and credit more generally. While not universal, men with income overwhelmingly have credit correlation and vice-versa.