Issues in Finance and Accounting - Assignment Example

Question One Part (a) Men under forty in the sample set = 75 Total number of agents in the sample set = 118 Probability of picking two men under forty = (75 / 118) x (74 / 117) = 0.402 = 40.2% Part (b) Men with incomes between 2,000 and 3,000 = 23 Number of men in the sample set = 98 Probability = (men with incomes between 2,000 and 3,000) / (number of men in the sample set) = 23 / 98 = 0.235 = 23.5% Part (c) Number of men under 35 and married = 37 Number of men required for survey = 5 Permutations are being utilized in order to bring out unique groups of 5 men out of a total of 37 men who meet the criteria. Number of ways to choose = 37P5 = 52307640 Question Two The highest income level for both groups (men and women) is 11,000. The detailed income levels of males and females for the population sample are shown in Appendix A. In order to tabulate frequencies to create histograms, a range of 500 has been chosen between consecutive range designations. The income levels start at rate that is less than 500 and go to the rate that I less than 11,500 to appreciate the full range of incomes. The range intervals, the frequencies and the cumulative frequency are presented below for both groups: Range Male Female Frequency Cumulative Frequency Cumulative 0-500 4 4 1 1 500-1000 3 7 4 5 1000-1500 8 15 5 10 1500-2000 25 40 9 19 2000-2500 16 56 0 19 2500-3000 13 69 0 19 3000-3500 8 77 0 19 3500-4000 4 81 1 20 4000-4500 3 84 0 20 4500-5000 4 88 0 20 5000-5500 4 92 0 20 5500-6000 2 94 0 20 6000-6500 1 95 0 20 6500-7000 0 95 0 20 7000-7500 1 96 0 20 7500-8000 1 97 0 20 8000-8500 0 97 0 20 8500-9000 0 97 0 20 9000-9500 0 97 0 20 9500-10000 0 97 0 20 10000-10500 0 97 0 20 10500-11000 0 97 0 20 11000-11500 1 98 0 20 Part (a) Men Women Mean 2635.95 1417 Standard Deviation 1701.16 751.55 Median 2217.5 1437.5 Part (b) The income distribution for men is roughly normal with greater skewness to higher income ranges after the median. In contrast, the income distribution for women is highly skewed towards higher income range. The median for men’s income is 2217.5 while the media for women’s income is 1437.5. On the other hand, the mean for men’s income is 2635.95 and the mean for women’s income is 1417 signalling a large difference in income between both groups. Men as well as women see highest income frequency for incomes between 1500 and 2000. Part (c) In the case of men’s income, the outliers are present beyond the income level of 7000. In the case of women’s income, the only outlier is in the 3500 to 4000 range. Men’s income is more affected by outliers as expressed by the standard deviation of 1701.16 while women’s income is not as deeply affected by outliers as expressed by the standard deviation of 751.55 (Freeman et al., 2007). Outliers for men’s and women’s income distribution can be dealt with by employing statistical corrections such as by converting the data to a normal distribution. Moreover, the outliers in the case of men can be seen as aberrations from the normal distribution of wealth and can be neglected altogether given the fact that these deviations affect the population sample’s credibility. The outliers are not only placed well away from the regular distribution but present an insignificant proportion of the overall sample set. It could be reasoned that these samples originate from clients who do not otherwise fit into the socio-economic group being studied. The same is true of women’s income. The aberration results in small frequency counts that are placed well above the regular income distribution pattern. Similar to the men’s case, the outliers in the case of women can be ignored to produce better results. Question Three The mean for the sample population’s age is 33.19 years and the standard deviation is 12.51 years. Part (a) Percentage of applicants under the age of 45 years = 82.76% Part (b) Percentage of applicants under the age of 25 years = 25.64% Percentage of applicants under the age of 35 years = 55.76% Percentage of applicants between the age of 25 years and 35 years = Percentage of applicants under the age of 35 years – Percentage of applicants under the age of 25 years Percentage of applicants between the age of 25 years and 35 years = 55.76 – 25.64 = 30.13% Part (c) Lower age limit for the oldest 25% of the population sample = Age of applicants under the 75% distribution mark Lower age limit for the oldest 25% of the population sample = 41.62 years Part (d) Percentage of applicants under the age of 45 years = 83.9% Percentage of applicants under the age of 25 years = 28.81% Percentage of applicants under the age of 35 years = 67.8% Percentage of applicants between the age of 25 years and 35 years = Percentage of applicants under the age of 35 years – Percentage of applicants under the age of 25 years Percentage of applicants between the age of 25 years and 35 years = 67.8 – 28.81 = 38.98% Normal Distribution (%) Actual Sample (%) Applicants under the age of 45 years 82.76 83.9 Applicants between the age of 25 years and 35 years 30.13 38.98 The answers for part (a) and part(b) tend to differ from each other based on the use of a normal distribution curve and the use of the actual sample. Using the normal distribution curve, the applicants under the age of 45 years are 82.76% while using the actual sample, the applicants under the age of 45 years are 83.9%. The slight difference between both values can be attributed to the outliers that tend to make the actual distribution different from a normal distribution. Moreover, the difference for both methods is sharper for applicants between the ages of 25 years and 35 years which are 30.13% and 38.98% respectively (Urdan, 2010). This indicates that the difference in skewness between the normal distribution and the actual population sample is sharper for the range between 25 years and 35 years compared to population under 45 years given the larger percentage difference. Question Four For the purposes of this question, the entries without any declared income levels are being assumed to be taken as zero. The sample size for men granted credit is 58 including 6 entries without any income declarations. This indicates that 10.34% of the population sample did not report its income including men who were granted credit. Similarly, the sample size of women not granted credit is 11 including 1 entry without any income declaration. This indicates that 9.09% of the population sample did not report its income including women who were not granted credit. Part (a) Alpha = 5% Mean for men granted credit = 2744.14 Standard deviation for men granted credit = 1866.02 Sample size = 58 Interval for men granted credit = 2744.14 ± 480.23 Alpha = 5% Mean for women granted credit = 1071.82 Standard deviation for women granted credit = 437.39 Sample size = 11 Interval for women not granted credit = 1071.82 ± 258.48 The final answers have been reported as the mean ± confidence interval for both cases. Part (b) In the case of both groups, the amount of respondents with undeclared incomes is nearly the same so any effects borne by the confidence interval calculation are somewhat similar. The mean for men granted credit is sizably larger as is the confidence interval while the mean for women not granted credit is smaller along with the confidence interval. The larger income levels of the men granted credit mean that missing income levels are bound to have a larger effect on the final answer. The lower income levels of the women not granted credit mean that missing income levels are going to have a lower effect on the final answer. The missing income levels have been supposed as zero, since men have larger income levels (as they were granted credit), the inclusion of zero values are going to have a significant effect. In the case of women not granted credit, the effect of using missing income levels as zero will have a lower effect for the reasons mentioned above. Part (c) The sample size for men granted credit is sizable larger than women not granted credit (58 versus 11 respectively) (Urdan, 2010). However, the proportion of missing income levels is nearly the same for both groups although it is slightly larger for men granted credit. The smaller sample size for women not granted credit means that the confidence interval calculation is less accurate when compared to men granted credit since the population sample is much larger. The larger sample size supporting men granted credit means that the accuracy for confidence interval calculation is greater. Bibliography Freeman, D., Pisani, R. & Purves, R., 2007. Statistics. 4th ed. New York: W. W. Norton & Company. Urdan, T.C., 2010. Statistics in Plain English. 3rd ed. London: Routledge Academic. Appendix A Males JOBINC ADDINC Total Income 2750 200 2950 1750 0 1750 5000 0 5000 3000 0 3000 2300 0 2300 3800 1100 4900 1955 0 1955 0 800 800 6250 110 6360 1500 0 1500 1500 0 1500 3000 0 3000 1300 210 1510 2085 100 2185 1575 0 1575 1850 0 1850 2500 0 2500 4500 0 4500 5000 300 5300 3375 175 3550 0 806 806 1750 300 2050 10000 1000 11000 2000 0 2000 2500 0 2500 2500 1620 4120 1300 350 1650 1625 0 1625 2000 0 2000 2750 0 2750 1625 0 1625 0 0 0 5000 2000 7000 1875 0 1875 2125 300 2425 4790 0 4790 0 0 0 5000 0 5000 1625 1000 2625 2250 0 2250 3625 0 3625 0 280 280 1750 100 1850 2650 0 2650 2250 0 2250 2500 0 2500 5000 0 5000 2575 0 2575 3340 115 3455 2250 0 2250 3750 0 3750 2750 0 2750 7500 0 7500 0 0 0 2500 0 2500 3435 0 3435 2080 0 2080 5500 400 5900 1350 0 1350 3750 0 3750 2160 0 2160 1425 260 1685 2500 0 2500 1100 0 1100 2500 0 2500 1500 0 1500 5560 0 5560 2375 0 2375 1000 240 1240 3250 0 3250 1000 0 1000 1880 0 1880 1650 0 1650 2500 116 2616 1000 0 1000 1650 196 1846 3165 0 3165 3000 0 3000 1300 0 1300 750 0 750 1750 0 1750 1750 0 1750 1885 0 1885 1875 310 2185 2250 0 2250 1125 0 1125 2000 0 2000 2000 0 2000 1125 0 1125 1875 0 1875 1500 175 1675 4500 400 4900 4000 0 4000 3250 800 4050 1650 0 1650 1750 0 1750 1750 0 1750 3000 0 3000 Females JOBINC ADDINC Total Income 1125 0 1125 3125 755 3880 1375 0 1375 1675 250 1925 1500 150 1650 1400 250 1650 1600 85 1685 1780 83 1863 560 0 560 875 0 875 1000 100 1100 1500 0 1500 1500 300 1800 875 85 960 1500 43 1543 1350 0 1350 0 0 0 1000 0 1000 1250 309 1559 940 0 940 Appendix B Men granted credit CLASS SEX JOBINC 1 1 2750 1 1 1750 1 1 5000 1 1 3000 1 1 2300 1 1 3800 1 1 1955 1 1 0 1 1 6250 1 1 1500 1 1 1500 1 1 3000 1 1 1300 1 1 2085 1 1 1575 1 1 1850 1 1 2500 1 1 4500 1 1 5000 1 1 3375 1 1 0 1 1 1750 1 1 10000 1 1 2000 1 1 2500 1 1 2500 1 1 1300 1 1 1625 1 1 2000 1 1 2750 1 1 1625 1 1 0 1 1 5000 1 1 1875 1 1 2125 1 1 4790 1 1 0 1 1 5000 1 1 1625 1 1 2250 1 1 3625 1 1 0 1 1 1750 1 1 2650 1 1 2250 1 1 2500 1 1 5000 1 1 2575 1 1 3340 1 1 2250 1 1 3750 1 1 2750 1 1 7500 1 1 0 1 1 2500 1 1 3435 1 1 2080 1 1 5500 Women not granted credit CLASS SEX JOBINC 0 0 875 0 0 1000 0 0 1500 0 0 1500 0 0 875 0 0 1500 0 0 1350 0 0 0 0 0 1000 0 0 1250 0 0 940 Read More