Inferential Statistics
Shreya Rauniyar
BUS708202002Ass2Template1.docx
Inferential statistics
BUS708 Assignment 2
Section 1: Introduction
The objective of this report is to conduct different statistical calculation and summary using stat key, hypothesis test, statistical test, confidence interval, compare graphical display from the Assignment 1 of Excel Sheet.
International students are the largest category of temporary migrants to Australia (Spinks 2010). However, international students have evolving expectations and place increased emphasis on post-study work experiences in the host labour markets and employability. A recent survey with over 1,150 international graduates showed that up to 76% mentioned access to post-study work rights was an important factor in their decision to choose Australia as their study destination (Tran, Rahimi, and Tan 2019). This increased emphasis on post-study work rights has been reflected in data about international student commencements in Australia since 2013. The main growth area of international student commencements for Australia since the introduction of the revised PSWR policy in 2013 has been the Masters by coursework programme. The top five citizenship countries of PSWR visa holders (India, China, Nepal, Pakistan, Vietnam) have also been the top five source countries of international commencements in Masters by coursework (China, India, Nepal, Pakistan, Vietnam) since 2013
Section 2
data presentation
This is to present the bar graph of the total in proportion of the lodgement methods.
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Row Labels |
Count of Lodgement method |
Proportion of Lodgement method |
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AGENT |
7419 |
74.19% |
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SELF PREPARER |
2581 |
25.81% |
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Grand Total |
10000 |
100.00% |
Inferential statistics
Thus, now we are going to calculate Standard Error, Critical Value with 95% confidence interval level using stat key.
Sample size (n) = 10000 Sample proportion of Self-preparer’s () = 0.2581 Standard Error (SE) = = 0.004375 Critical value = 1.96 95% Confidence Interval = 0.2581 (1.96)(0.004375) = (0.266675 ,0.249525)
Did around 25% of taxpayers in 2013-2014 self-prepare their tax return?
Based on the above interpretation, we can conclude that yes there is enough evidence that around 25% of the taxpayers in 2013-2014 self-prepared their tax return.
Section 3:
In this section, we are going to calculate and summarise sample size, mean, standard deviation, minimum, Q1, median, Q3 and maximum from the Dataset1 and the box and whisker plot diagram using stat key respectively.
data presentation
It presents salaries and wages in the form of outliers for the year with the suitable diagram.
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Inferential statistics
So, now sample size , sample mean, sample standard deviation and hypothesis test is carried out using stat key.
Sample size (n) = 10000 Sample mean of Salary and Wages (X bar) = 44148.464 Sample standard deviation of Salary and Wages (s) = 52350.471
Test-statistic
p-value = 0.500 From Stat key, Theoretical Distributions: t, with df = n-1 = 9999
Is the average salary of taxpayers in 2013-2014 less than $45,000?
There is enough evidence to prove that yes the average salary of taxpayers in 2013-2014 is less than $45000.
Section 4:
data presentation
In this section, different number of numerical summary is calculated respectively using he dataset 1 linking it with stat key.
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Statistics |
Agent |
Self-preparer |
Overall |
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Sample Size |
236 |
68 |
304 |
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Mean |
64747.602 |
71492.603 |
66256.35 |
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Standard Deviation |
26769.665 |
18781.347 |
25332.1 |
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Minimum |
0 |
0 |
0 |
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Q1 |
64975.5 |
74913.5 |
70939.5 |
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Median |
75741 |
76506.5 |
75902 |
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Q3 |
77795 |
78378.5 |
77896.5 |
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Maximum |
127212 |
89269 |
127212 |
Inferential statistics
Please write something here to introduce what you will perform.
Step 1:
H0: All means are equal H1: Not all means are qual
Step 2:
ANOVA Table
So, the test statistic =
Step 3:
p-value = 0.000 (from Stat key with numerator df =n-1= )
Step 4
Reject H0
There is strong evidence of
Section 5:
data presentation
Thus, in this section, data is analysed under regression using all the data from dataset 1 showing the total income amount and total deduction amount in the scatter plot diagram below.
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.372948432 |
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R Square |
0.139090533 |
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Adjusted R Square |
0.138756589 |
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Standard Error |
42356.23197 |
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Observations |
2580 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
7.47236E+11 |
7.47E+11 |
416.5077 |
6.0781E-86 |
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Residual |
2578 |
4.62506E+12 |
1.79E+09 |
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Total |
2579 |
5.3723E+12 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
41717.23982 |
880.3681554 |
47.38613 |
0 |
39990.93946 |
43443.5402 |
39990.9395 |
43443.5402 |
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353 |
3.754003815 |
0.183942976 |
20.40852 |
6.08E-86 |
3.393312865 |
4.11469477 |
3.39331286 |
4.11469477 |
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Inferential statistics
Correlation coefficient = 0.37, it is nowhere close to 1, so there is weak and positive correlation between total income and deduction amount, respectively.
Coefficient determination = 0.14 so, 14% of the variation in total deduction amount is explained by total income amount.
p-value = 6.0781E-86 which is very very less amount.
Is there any relationship between total income amount and total deduction amount for self-preparer?
Hence, based on the discussed things above, there are many reasons to prove that there is relationship between total amount and total deduction amount for self-preparer.
Section 6:
data presentation
The following is the data information which is collected from social media like email, facebook, whatsapp and linkedin from a sample of 30 international students in Australia who are male and female.
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Count of Gender |
Column Labels |
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Row Labels |
F |
M |
Grand Total |
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N |
10 |
6 |
16 |
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Y |
6 |
8 |
14 |
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Grand Total |
16 |
14 |
30 |
Inferential statistics
So, this is Null Hypothesis and Alternative Hypothesis
H0: 1.157 H1: 1.157
Test-statistic = 1.157 (using Stat key)
p-value = 0.282(From Stat key, df = (2-1) (2-1) = 1
Is there a relationship between the gender of international students and whether they would use a tax agent?
The above interpretation helped us conclude that since 2 is 1.157, this is right-tailed and shows the positive relationship between the gender of international students and whether they would use a tax agent.
Section 7: Conclusion & Recommendation
This report concludes that , In Section 2 we found enough evidence that supported saying 25% of taxpayers in 2013-2014 self-prepare their tax return, In Section 3, we found and concluded that the average salary of taxpayers in 2013-2014 less than $45,000, In Section 4, , In Section 5, we concluded that there is positive relationship between total income amount and total deduction amount for self-preparer, In Section 6, we concluded that there is a relationship between the gender of international students and whether they would use a tax agent.
Those findings can be used to evaluate that how many international students are migrating in Australia, how many students are loyally paying the tax to the government and also may sure that they are not voiding any rules that they are obliges to follow in the territory respecting the culture and system. This report will be particularly useful for the immigration, different tax agents who are out their helping international students lodge their tax return
Further research that can be conducted after this tax lodgement could be how many students migrating in Australia do job in tax and pay tax to the Australian Government.
References
1. AEI . 2020. “International Student Data December 2019” . Canberra : Australian Government. [Google Scholar]
2. Australian Government . 2018. Student Visa and Temporary Graduate Visa Programme Quarterly Report – Ending at 30 June 2018. Department of Home Affairs, Canberra. https://www.homeaffairs.gov.au/research-and-stats/files/student-visa-programme-report-2013-14-to2014-06-30.pdf [Google Scholar]
Self Preparer scatter chart
Total income amount S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S 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S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S 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4940 0 377 6692 316 120 1025 602 0 827 917 0 54 2140 1198 0 0 172 0 113 628 592 476 0 0 683 343 2138 0 0 1073 0 6214 4892 162 0 1217 269 6575 0 238 2067 1278 326 0 850 1093 3926 320 3346 256 0 1966 0 0 0 267 1674 3272 1665 1121 184 282 0 0 657 0 963 533 588 0 4 22 3134 0 2400 0 0 5389 269 0 4480 12317 93 412 3658 7330 2264 0 270 379 0 0 0 2311 2114 0 0 262 1289 276 822 1101 298 93 4741 332 1650 1052 962 0 2367 0 0 72 339 145 634 0 0 0 0 270 103 249 0 1011 786 0 0 294 1759 2389 3509 190 1903 279 284 36 454 1201 147 0 3368 2460 243 3957 0 10570 417 138 138 1237 0 362 0 273 1400 244 0 1299 4183 0 4945 497 2182 0 4374 1560 825 282 888 3245 247 360 65 0 35362 317 498 0 302 90 578 8979 0 53 0 897 233 5336 0 5251 0 755 1315 1012 0 867 70 0 0 164 0 965 115 2826 350 170 277 1816 190 1989 315 0 878 773 696 3813 336 845 264 0 10037 132 126 575 0 3013 1510 509 491 0 961 0 552 0 0 1985 0 813 2334 366 2605 11633 475 0 314 358 308 6749 0 0 3264 280 0 3290 0 2254 0 0 818 0 213 5147 0 6489 0 0 2435 775 2624 0 0 540 8821 121 0 0 693 314 651 2221 4744 0 2665 2969 430 0 542 55 3372 0 4307 643 0 0 19 0 207 126 0 51 0 0 960 282 0 32 287 0 0 918 274 4956 1067 198 394 0 931 709 0 6025 3921 402 0 131 0 0 695 41 819 277 0 293 2633 3930 218 0 0 8953 959 0 0 699 735 738 0 3787 2476 210 0 2599 259 0 0 3697 22 0 104 7550 3802 305 211 938 162 0 1626 18782 0 655 284 0 637 844 0 191 335 0 0 9 0 6978 7691 4142 466 61 0 44 1604 224 737 804 0 0 600 111 158 156 0 2052 2206 3623 0 2306 128 1891 321 245 138 138 1319 3221 0 437 0 0 93 7475 0 840 895 0 18 230 5503 188 3426 318 446 0 1130 2138 525 3714 1302 19 329 0 691 3434 0 321 1134 9892 106 3829 12400 0 0 308 316 272 119 0 515 6375 3397 659 9866 1323 27 0 6917 1395 0 632 294 0 111 229 1133 0 1150 0 3593 85 331 4592 612 0 5058 224 230 350 3829 197 0 763 758 201 520 3293 4401 1640 2531 220 0 717 0 0 275 0 400 806 257 608 0 0 403 6624 319 326 0 4489 524 2425 32 3708 1803 188 1836 399 803 52 328 0 3515 250 1269 0 1560 0 21233 697 810 272 0 0 276 4259 170 0 521 344 1265 132 102 3 8160 3692 0 5852 49 2226 655 531 173 0 1180 55 878 322 3138 899 2020 738 2288 1955 1693 280 866 19 50 3371 2009 0 264 0 337 1823 2975 0 188 53 222 286 168 3315 1009 1378 3619 451 0 376 660 426 2677 762 0 47 548 279 1040 801 2257 0 23 0 263 0 625 544 2319 842 12442 0 0 332 274 0 4196 9074 290 919 0 1284 6210 1173 327 4449 0 472 0 0 0 0 281 0 9136 2139 289 0 1933 692 861 0 0 0 0 2114 328 243 46 338 500 3291 4340 0 671 4712 1274 2332 0 1517 270 646 3706 13096 984 290 54 1008 72 894 3621 0 162 0 6277 0 0 0 354 1242 324 0 606 650 2692 1755 0 6641 0 0 5504 59 957 926 10508 2126 179 406 2282 6234 2271 1196 129 788 2480 442 0 595 866 125 1247 683 0 1792 1197 606 0 0 198 5737 107 3748 4771 0 9114 0 3011 271 543 99 574 0 0 199 137 160 0 1892 11 1352 620 12777 1636 3368 165 364 0 193 0 441 0 0 3979 9836 307 0 0 0 214 0 7327 488 1354 0 262 0 1973 2698 0 0 8749 480 444 3171 500 0 0 683 4123 311 0 392 2009 12329 0 3430 0 4156 0 276 778 115 1040 164 10826 283 446 406 383 7098 0 3778 0 328 322 0 0 267 450 5102 1149 264 0 4117 0 37 1466 931 91 898 0 202 9499 55 329 20621 1054 0 24507 1092 0 5777 744 1552 0 0 4376 3502 1217 13419 156 0 264 274 0 10360 1199 262 160 0 943 1578 0 0 6243 854 1835 1482 3461 381 445 326 160 324 0 0 1015 0 0 0 4432 147 301 0 278 485 38 0 0 905 2516 1241 0 293 4876 0 0 8253 261 1153 325 0 3388 0 0 1344 5182 634 259 3183 4196 0 9618 21 0 201 284 243 280 3305 0 547 922 0 2355 18 1320 262 704 322 4486 0 801 0 0 995 962 0 1161 1098 0 7558 780 0 13221 83 0 250 0 603 0 485 4870 1048 150 0 1641 110 0 949 1083 0 3664 130 1837 45 5369 752 1942 3496 0 9730 91 173 262 0 8752 441 1307 0 9537 0 7369 2013 618 0 0 25345 6832 6201 436 0 1512 0 0 49 2338 0 2655 0 10326 1022 274 0 0 318 604 4 0 3962 1273 276 1617 0 0 0 0 7236 721 685 270 1511 0 0 510 271 4351 4268 0 3730 3874 21 4390 429 6404 0 0 0 6698 56 181 18 0 882 341 184 0 2836 703 20522 280 0 14985 385 1290 804 154 236 651 2468 696 0 46 986 1009 577 1420 0 3198 336 0 5659 3576 0 4395 0 0 0 274 0 2193 0 4662 579 0 0 0 44 1616 0 83 6237 0 2027 643 427 272 4947 716 0 0 112 0 1659 193 0 703 580 0 8147 0 260 2457 2082 501 653 725 6532 1499 1085 0 163 11511 2172 1347 635 751 159 288 265 0 0 14010 867 0 1093 7008 228 18 2080 13 112 0 155 463 602 30 13054 3856 0 679 1364 879 1886 2151 163 5613 2650 3805 0 38 0 22 1126 99 494 0 383 0 297 0 0 0 5011 218 94 91 1640 1186 411 867 1027 1251 0 248 241 0 0 480 5934 7987 991 4332 1648 4323 677 557 0 0 51 59 95 0 0 8634 6349 184 0 0 0 214 270 7847 4007 3873 0 118 2014 0 0 996 1120 0 3296 1258 868 5660 0 0 0 4571 528 22 278 256 330 303 44 0 32499 59 0 0 3886 0 674 118 0 689 350 0 688 0 6045 0 2917 0 1604 0 783 138 0 218 592 377 0 0 0 0 1239 0 6793 152 713 252 27176 1103 0 0 0 172 30515 0 0 0 140 6304 0 0 328 5029 391 0 323 792 4222 727 0 858 222 8336 9295 3095 0 0 521 0 2687 717 70 729 0 7335 1122 279 534 0 0 3120 1787 0 399 2503 0 0 158 0 4003 1859 782 6200 635 0 1367 186 1480 0 278 0 0 2822 724 9953 308 164 279 0 15763 10559 291 2807 103 4 612 7437 158 122 0 320 3071 0 77 202 0 2292 0 379 286 107 0 4526 0 355 0 0 0 112 0 696 435 4419 171 1094 4367 0 9135 0 7262 247 271 268 71 774 385 509 0 1445 0 0 761 4003 971 482 1161 405 0 0 527 0 0 424 606 290 136 0 2846 378 695 0 1374 0 0 0 673 3294 12167 0 3895 0 3396 323 0 425 633 71 0 1466 0 7525 242 685 270 1700 0 335 168 1013 677 0 140 3571 1511 0 160 3512 316 0 2500 128 1753 775 951 4536 107 10930 68 0 2654 0 0 2155 94 0 65 3033 903 233 1803 0 768 4347 1272 0 291 5426 433 9 0 0 275 0 11222 375 438 3569 422 318 488 0 223 238 991 397 0 0 0 395 0 236 0 366 44 117 106 0 111 214 0 1034 271 10617 115 0 5437 310 0 4947 0 4535 0 0 1781 0 0 0 359 1528 1250 515 292 4621 433 355 3744 2891 0 5473 11398 662 141 510 323 420 7755 52 303 69 113 83 6470 2181 528 5386 103 957 979 4684 3014 4620 0 124 4443 290 0 1978 65 703 77 0 5094 264 0 142 0 1434 0 3347 430 1150 417 112 4277 5253 407 0 2740 0 0 0 16477 56 377 251 976 264 889 568 0 1014 140 5909 0 0 1458 4269 0 1196 0 1033 1000 2392 213 939 6270 0 12 696 4612 276 1023 138 271 5135 676 1083 60 1934 175 0 0 913 0 4409 336 2517 2785 224 2317 1462 3446 379 795 5755 162 338 0 284 168 148 0 3622 504 211 297 325 0 162 423 160 280 0 0 774 1125 113 1123 486 0 105 103 11 0 55 0 904 0 179 0 6 0 272 1591 139 1423 0 0 0 321 197 0 828 939 0 298 5073 1842 487 0 487 2363 380 632 1980 0 55 3882 368 0 15159 854 8384 55 0 2311 0 1588 0 421 5248 0 315 328 109 85 0 950 907 0 1060 620 0 43 232 0 141 255 408 956 1039 0 385 1384 302 0 1535 141 0 414 1783 22 162 256 722 0 467 3848 540 100 464 3515 667 0 0 162 0 326 787 0 1667 0 164 159 570 459 0 2299 872 323 0 212 8802 0 0 0 318 1607 0 71 1710 273 0 132 80 12 2622 138 0 21500 148 3356 0 7052 201 0 10458 817 4942 2534 0 286 0 0 624 3683 0 0 2688 148 3561 18 4099 346 45 1800 355 0 6611 0 242 864 218 1754 161 435 16 664 438 13716 1883 0 268 133 1508 0 0 54539 3004 5601 0 0 1182 319 1052 163 0 11 2212 1224 4178 729 21 11182 4404 0 0 0 875 68 256 2435 314 0 0 0 45 443 276 326 0 12992 0 324 34 4449 629 0 0 0 570 0 9 4883 789 258 0 0 94 0 294 0 1267 433 299 282 894 3431 463 0 561 0 0 143 803 749 0 1794 199 0 0 0 0 1418 609 1745 10814 1607 1143 244 0 1571 0 4024 2221 24 6143 619 3082 210
F N Y 10 6 M N Y 6 8
Count of Lodgment method
Count of Lodgment method
AGENT SELF PREPARER 7419 2581 Proportion of Lodgment method AGENT SELF PREPARER 0.7419 0.2581
