Task 6 (7 marks)
A reminder, in this task, to make sure that you show any necessary working.
Failure to do so will result in the loss of marks.
(a) By reference to numerical summary measures in the Descriptive Statistics table obtained in Task 5, provide three pieces of distinct evidence that might suggest that your sample “Sold Price” data has been obtained from a normally distributed population. What is your conclusion? Note: Make sure your three pieces of distinct evidence only contain one relating to the shape of the sample data.
(b) Regardless of your conclusion in (a), assume your sample “Sold Price” data have been obtained from a normally distributed population, and calculate, using Standard Normal tables, approximately how many “Sold Price” data values in your sample you would expect to lie within 1.5 standard deviations of the mean (i.e. between z = –1.5 and z = +1.5).
(c) Use your sorted “Sold Price” sample data from Task 4, and the mean and standard deviation from the Descriptive Statistics table of Task 5, to manually count the number of “Sold Price” data values in your sample that lie within 1.5 standard deviations of the mean. State whether this count matches, approximately, your answer to (b) and hence whether this result confirms (or not) your conclusion in (a).
Task 7 (7 marks)
(a) Use Excel to produce a Descriptive Statistics table for the “Sold Price” variable in your sample suitable for constructing an interval estimate of the population mean “Sold Price”. Hence determine:
(i) A point estimate of the mean “Sold Price” of the population of properties.
(ii) A 90% confidence interval estimate of the mean “Sold Price” of the population of properties.
(b) Make a brief verbal statement explaining the meaning of the confidence interval estimate obtained in (a) in the context of the variable in this task.
(c) If the population mean “Sold Price” is actually 650 ($000s), would you consider the interval estimate obtained in (a), to be satisfactory? Explain why or why not.
Task 8 (6 marks)
(a) By reference to the Descriptive Statistics table obtained in Task 7, determine a 99% confidence interval estimate of the mean “Sold Price” of the population of properties using the following formula:
(sample statistic) (critical z or t) (standard error of the sample statistic)
(b) Comment on the precision of this interval, in particular, compare the precision associated with this interval with that obtained in Task 7. Explain why the direction of the change in precision that you have observed in these two intervals ought to be obvious prior to constructing the two intervals.
Task 9 (7 marks)
(a) Use Excel to produce a Descriptive Statistics table for the brick veneer properties in your sample suitable for constructing an interval estimate of the population proportion of brick veneer properties. Hence determine:
(i) A point estimate of the proportion of brick veneer properties in the population.
(ii) A 99% confidence interval estimate of the proportion of brick veneer properties in the population.
(b) Make a brief verbal statement explaining the meaning of the confidence interval estimate obtained in (a) in the context of the variable in this task.
(c) If the population proportion of brick veneer properties is actually 42%, would you consider the interval estimate obtained in (a), to be satisfactory? Explain why or why not.
PN V1 V2 V3 V4 V5 V6 V7 V8
1 4 0 1 1 4 648 586
2 1 0 2 1 5 380
3 1 0 1 2 4 453 389
4 4 0 1 1 3 480 410
5 2 1 1 3 5 675 435 379
6 2 1 1 2 6 590 462 391
7 2 1 3 2 4 385 295 271
8 2 1 1 2 5 360 432.5 371
9 2 1 1 1 6 604 350 279
10 2 0 1 1 2 239.5 221
11 3 1 1 3 7 745 825 761
12 3 1 1 1 5 465 911 760
13 3 0 3 2 3 475 425
14 1 4 4 641 277.5 253
15 2 1 1 3 5 585 563 491
16 3 0 1 1 5 781.5 717
17 3 0 1 2 7 937 777
18 3 1 3 2 8 796 386 319
19 3 0 3 2 5 363 308
20 3 1 1 2 7 730 1190.5 1015
21 1 0 1 1 4 250 375 307
22 3 0 1 1 4 345 608 540
23 3 0 1 2 5 700 650
24 3 0 1 1 4 881 830
25 3 1 1 2 9 1071 1360 1196
26 3 1 1 3 8 727 725 659
27 3 1 1 3 6 642 530 457
28 3 1 1 1 6 1039 450 392
29 3 1 1 3 6 692 882 809
30 3 1 1 3 5 605 704.5 636
31 3 1 1 2 6 730 840 771
32 2 1 1 3 5 650 396 336
33 3 1 1 3 6 740 2750 2621
34 3 1 1 1 8 687 1335 1224
35 2 1 1 3 4 580 328 269
36 2 3 4 512 118.95 103
37 2 0 1 1 4 430 374
38 1 1 1 3 5 274 715 641
39 1 1 4 427 750 697
40 1 0 1 1 4 467 394
41 3 1 1 2 7 618 620 546
42 1 0 1 2 5 452.5 392
43 2 1 3 2 4 315 280 255
44 2 1 3 2 7 630 430 360
45 3 1 1 3 5 430 583.5 511
46 3 1 1 2 5 590 620 565
47 2 2 4 808 315
48 3 0 1 1 4 450 389
49 3 1 1 3 7 875 1606 1474
50 4 1 1 1 4 149 820 749
51 3 0 1 1 2 336 276
52 2 1 3 2 4 320 310 236
53 3 1 3 2 4 350 245 218
54 3 1 1 1 5 585 1108 913
55 3 1 1 1 5 443 873.5 818
56 3 1 1 3 4 632 612.5 550
57 3 0 1 2 4 317 247
58 3 0 2 2 5 825
59 4 1 4 1 5 229 800 736
60 1 1 1 1 5 245 627.5 558
61 1 1 1 2 5 520 476 423
62 4 0 1 1 3 562 489
63 1 1 3 2 5 530 316 256
64 3 1 3 2 6 406 348 298
65 3 1 3 2 7 891 415 348
66 3 1 2 2 6 864 315
67 2 1 1 2 6 538 270 254
68 1 0 2 1 5 550
69 3 1 1 2 9 641 561 498
70 4 0 1 1 4 715 645
71 3 1 1 2 8 656 775 700
72 3 1 3 2 7 858 627.5 563
73 3 1 2 2 9 979 520
74 1 1 1 1 7 1370 1611 1438
75 3 1 4 1 5 433 900 828
76 3 1 3 2 6 2784 691 628
77 3 0 4 1 3 431.5 365
78 3 3 4 3968 340 290
79 1 1 1 2 5 288 340 266
80 1 1 1 1 6 985 1175 1034
81 1 1 3 1 9 900 2150 1996
82 1 1 3 1 6 411 630 558
83 2 1 2 3 5 770 690
84 3 1 1 3 5 370 740.5 673
85 1 1 1 1 5 1380 911 753
86 3 1 4 3 4 732 347 288
87 4 0 1 1 4 601 544
88 4 1 1 1 5 160 890 838
89 4 0 4 1 4 412.5 341
90 2 1 1 1 6 373 740 678
91 2 1 4 3 5 360 745 694
92 2 0 4 2 4 410 337
93 3 0 1 2 5 466 396
94 3 0 4 1 4 430 379
95 3 1 1 1 6 652 1200 1068
96 3 1 1 1 9 836 1301 1146
97 3 0 1 1 3 705 630
98 3 1 3 3 5 356 1070 886
99 3 1 1 2 9 500 1085 930
100 3 1 2 2 7 542 490
101 3 1 4 2 7 703 960 817
102 1 0 1 2 4 350 277
103 1 1 1 2 6 500 460 399
104 1 1 3 2 5 600 455 383
105 1 1 1 2 5 451 460 396
106 1 1 1 2 6 618 444 369
107 1 1 2 2 8 879 1200
108 1 1 3 2 5 582 432 368
109 1 2 4 1220 350
110 1 0 4 2 5 375 312
111 1 1 1 3 5 650 440 374
112 1 1 1 2 5 600 455 392
113 3 0 1 2 4 581 509
114 3 1 4 1 5 604 1230 1111
115 3 1 2 2 5 613 450
116 3 1 1 1 5 845 1800 1681
117 3 0 1 1 6 880 827
118 3 0 1 1 4 468 413
119 3 0 3 1 2 310 239
120 3 0 1 2 5 491 439
121 3 0 1 2 3 342 289
122 3 1 1 3 5 224 626 572
123 3 1 4 780 415 362
124 1 1 1 2 7 927 1552.5 1395
125 1 1 1 3 5 581 755 704
126 1 1 1 2 5 604 419 361
127 1 0 1 2 5 319 255
128 3 1 1 3 7 591 671.5 617
129 3 1 4 2 8 675 1410 1267
130 3 1 3 1 5 733 725 653
131 2 1 4 2 7 646 370 308
132 2 1 3 2 4 876 390 340
133 2 1 3 2 9 2000 825 765
134 3 1 1 3 7 790 831 777
135 3 1 1 3 6 1021 661 597
136 3 1 3 2 6 512 552 490
137 1 0 1 2 4 445 381
138 1 0 1 2 5 670 614
139 1 1 3 3 5 645 570 505
140 1 1 1 1 8 1092 1885 1755
141 1 1 1 1 10 815 2000 1870
142 2 1 3 2 8 885 425 363
143 2 1 1 1 7 636 542 486
144 2 1 1 3 6 585 552 480
145 2 1 2 1 8 548 720
146 4 1 1 3 3 248 615 554
147 4 1 1 1 4 160 590 533
148 4 0 1 1 3 445 378
149 4 0 4 1 3 385 317
150 3 1 1 1 5 412 1126 989
151 3 0 1 1 3 435 381
152 3 1 1 1 8 657 1410 1219
153 3 1 2 1 12 2440 1500
154 3 1 3 1 6 720 1380 1235
155 3 0 1 2 3 482 427
156 3 1 2 2 10 645 1150
157 3 0 4 1 5 720 653
158 3 3 4 20000 2650 2458
159 2 1 3 2 5 557 300 278
160 2 1 1 3 4 330 636.25 572
161 2 1 4 3 4 296 633 564
162 2 0 3 2 4 385 320
163 2 3 4 1085 132 105
164 2 1 4 1105 152 127
165 1 1 1 1 5 397 351 283
166 1 1 4 1 5 697 400 330
167 1 0 3 2 3 357 305
168 1 0 3 2 3 379 314
169 1 1 1 3 6 300 479.5 423
170 1 1 3 3 5 589 525 455
171 2 1 1 3 6 535 465 406
172 2 1 1 1 5 528 601.5 535
173 2 1 2 1 4 280 750
174 2 1 3 2 8 601 659 589
175 3 1 1 3 4 367 1059 918
176 3 1 1 1 8 699 1424 1275
177 3 0 1 1 6 736 664
178 3 0 1 1 3 374 312
179 3 0 1 2 5 795 721
180 3 1 1 1 8 810 2050 1924
181 3 0 4 1 5 936 803
182 2 1 1 1 9 487 750 684
183 2 1 1 3 5 615 724 659
184 2 1 4 1 4 200 460 407
185 2 1 3 3 5 330 510 448
186 3 1 1 1 5 319 805 736
187 3 0 4 2 3 331 267
188 2 1 1 2 4 742 426.5 362
189 4 0 1 1 2 1100 988
190 4 0 3 1 5 560 510
191 2 1 1 2 7 650 270 253
192 2 3 4 496 114 98
193 2 1 3 2 6 580 230 219
194 2 3 4 448 104 91
195 2 1 1 2 5 700 236 207
196 2 1 1 2 6 600 188.5 171
197 2 3 4 600 125 97
198 2 3 4 560 112 87
199 3 0 1 1 3 420.5 367
200 3 0 4 2 5 480 427
201 1 1 1 2 7 20000 1010 826
202 4 0 1 2 2 360.5 306
203 1 0 1 2 4 291.5 265
204 1 1 2 2 5 531 550
205 1 0 3 2 5 340 267
206 3 1 1 3 6 1018 756 702
207 3 0 4 2 6 445 393
208 3 0 3 2 5 450 396
209 3 1 1 1 5 603 951 753
210 3 1 1 2 6 603 1036 933
211 3 1 1 1 5 692 725 670
212 3 1 1 2 5 578 718 662
213 3 1 1 3 8 719 851 787
214 3 1 3 1 5 1241 1225 1060
215 1 1 1 3 5 412 379 313
216 1 1 3 3 5 1304 602 544
217 1 1 3 2 8 923 532.35 472
218 2 0 1 1 2 285.5 263
219 2 0 1 1 4 500 436
220 2 1 3 3 4 236 610 541
221 3 0 1 2 5 486.5 417
222 3 1 1 2 6 730 650 590
223 3 1 4 1450 1360 1208
224 3 1 1 1 5 997 888 832
225 3 1 4 2 5 796 900 850
226 3 1 3 2 4 653 516.82 465
227 3 0 3 2 5 490 440
228 3 1 1 1 4 435 596 536
229 3 1 3 1 3 468 711 636
230 3 1 2 2 9 4441 650 597
231 2 1 1 3 6 291 603 546
232 2 0 1 2 6 670 610
233 2 0 2 2 5 475
234 2 1 4 3 5 350 410 359
235 2 0 3 1 5 567.86 498
236 1 0 1 2 5 710 639
237 1 1 3 2 7 900 900 844
238 3 0 1 2 4 262.5 233
239 3 0 1 2 4 238 215
240 3 1 1 2 5 890 525 457
241 4 1 1 1 4 125 782 716
242 4 0 1 1 4 516 449
243 4 0 1 1 2 370.5 299
244 4 0 4 1 2 297 287
245 1 1 1 2 5 1632 425 351
246 1 1 3 2 6 4771 760 698
247 1 1 1 1 4 180 649.25 595
248 1 1 1 1 7 500 2020 1896
249 1 1 1 3 4 370 853 785
250 1 1 1 1 5 278 835 766
251 1 1 1 2 3 77 490 437
252 1 0 4 2 3 425 350
253 3 0 1 2 4 406 335
254 3 1 1 3 5 372 502 434
255 1 1 2 2 5 295 710
256 1 1 4 3 6 677 582 523
257 1 1 3 2 6 697 505 447
258 3 1 1 1 4 574 755 700
259 3 1 4 809 720 651
260 3 1 3 1 7 645 665 601
261 3 0 2 1 4 460
262 3 1 3 3 6 607 641 579
263 3 1 1 1 5 566 805 731
264 3 1 4 3 5 308 621 550
265 3 1 3 3 5 220 480 405
266 4 1 3 1 7 285 1311 1182
267 1 1 1 3 5 971 785 732
268 1 0 1 2 4 441 381
269 1 1 1 2 5 687 642 572
270 1 1 1 3 4 495 480 430
271 1 1 1 2 5 1079 795 742
272 1 1 3 2 3 165 430 357
273 1 1 1 3 6 608 741 669
274 1 1 3 2 5 626 595 538
275 1 1 4 1024 481.5 418
276 2 1 1 2 5 380 363 289
277 2 1 3 2 5 400 382 319
278 2 3 4 402 190 160
279 4 0 1 1 4 865 814
280 4 0 1 1 4 710 649
281 4 1 1 3 3 115 711 654
282 4 1 2 2 6 278 690
283 4 1 4 3 6 185 850 775
284 4 1 4 1 4 167 675 618
285 3 0 1 1 3 686 623
286 3 0 1 2 5 1060 921
287 3 1 2 1 8 343 950
288 3 0 4 2 4 705 641
289 1 1 1 1 4 390 450 388
290 1 1 1 3 3 239 446 391
291 1 0 1 1 3 401 336
292 1 1 1 1 4 550 436 365
293 1 1 1 3 5 712 631 577
294 1 0 4 2 3 392 322
295 1 1 1 3 6 578 424 369
296 1 0 1 2 5 390 340
297 1 1 1 3 5 385 387.5 332
298 1 1 1 2 7 504 746 687
299 1 0 1 2 4 358.5 306
300 1 0 1 2 4 330 278
301 1 1 1 2 5 446 432.5 369
302 1 0 1 2 4 350 284
303 1 1 2 2 6 750 825
304 1 0 2 2 4 440
305 1 0 4 2 4 351 279
306 1 0 3 2 4 415 358
307 1 0 3 2 4 340 277
308 1 0 3 2 6 427 364
309 4 0 1 1 2 354 279
310 4 0 1 1 2 455 386
311 4 1 1 3 4 162 752 680
312 4 1 1 1 4 207 785.5 730
313 4 1 1 3 4 140 794 733
314 4 1 1 1 4 166 840 771
315 4 0 1 1 3 501 451
316 4 1 1 1 4 96 760 697
317 4 1 1 1 4 189 915 797
318 3 1 1 3 6 703 501 433
319 3 1 2 2 5 577 480
320 3 1 2 3 7 2405 930
321 1 0 1 2 5 590 524
322 1 1 1 2 6 584 470 418
323 1 1 2 1 7 620 725
324 1 1 3 2 6 605 503 442
325 3 0 1 2 6 605 536
326 3 1 3 1 7 695 1125 994
327 3 1 3 2 7 700 845 788
328 2 1 1 3 4 141 572.5 509
329 2 1 2 1 5 322 310
330 2 0 4 2 4 441.5 382
331 4 1 1 3 4 122 882.5 819
332 4 1 1 1 6 133 917 725
333 1 0 3 2 6 342.5 287
334 1 1 3 2 7 634 481 428
335 1 1 3 2 7 805 461.25 391
336 3 0 1 1 3 495 420
337 3 0 1 1 3 504 446
338 3 1 1 3 5 255 880 827
339 4 0 1 1 4 560 488
340 2 1 1 3 6 442 670 601
341 3 3 4 510 348 288
342 2 1 1 2 5 550 353 292
343 2 1 1 2 6 766 439 376
344 2 1 3 2 4 300 295 284
345 2 1 3 3 4 620 360 304
346 4 0 1 1 1 209 194
347 4 0 1 1 3 323 266
348 4 0 1 2 2 457 385
349 4 0 1 1 2 286 257
350 4 0 1 1 3 346 296
351 4 0 1 1 4 600 543
352 4 0 2 1 2 425
353 4 0 3 1 5 740 672
354 3 0 1 1 3 409 359
355 3 0 1 1 4 544.5 493
356 3 1 4 1 3 132 618 548
357 1 1 1 2 5 751 1070 936
358 1 1 1 3 6 650 697 627
359 1 1 4 1 7 725 645.55 593
360 1 1 3 2 6 12000 640 573
361 1 1 3 2 6 830 459 397
362 1 1 3 2 6 630 305 255
363 1 1 3 2 4 250 260 231
364 2 1 1 3 5 450 418 363
365 2 1 4 3 5 405 430 357
366 2 1 1 3 5 600 358.5 307
367 2 1 1 3 4 604 335.5 261
368 2 1 1 3 5 630 426 366
369 2 1 4 3 5 580 375 313
370 2 1 4 3 6 635 450 400
371 2 3 4 1160 265 238
372 2 1 1 2 5 550 400 341
373 2 3 4 810 300 290
374 3 1 2 2 9 766 950
375 3 1 3 3 9 766 1180 1052
376 2 1 1 2 5 1000 480 410
377 2 1 1 2 6 632 400 345
378 2 1 4 2 6 702 450 392
379 2 1 4 2 8 650 518 445
380 2 1 3 2 6 684 410 341
381 2 1 3 2 6 672 400 332
382 2 1 3 2 5 599 370 299
383 3 1 1 2 9 4095 1900 1722
384 3 0 4 2 4 437 375
385 3 1 3 2 8 655 1215 1029
386 3 1 1 2 5 737 610 548
387 3 0 4 2 7 685 615
388 3 0 3 2 5 510 458
389 1 1 1 1 5 584 361 306
390 1 1 3 1 5 540 350 289
391 1 0 1 1 3 410.5 356
392 1 0 1 1 3 467 414
393 1 0 4 1 3 315 260
394 3 0 1 1 4 1200 1063
395 3 1 2 3 8 527 720
396 1 1 1 2 6 530 420.5 361
397 1 0 3 1 6 317 246
398 3 1 1 2 5 596 555 486
399 3 1 1 2 5 627 535 485
400 3 1 4 3 8 1235 675 610