MINITAB needed. Please show everything The file Toronto.mtw (added at the end) c
ID: 3039907 • Letter: M
Question
MINITAB needed. Please show everything
The file Toronto.mtw (added at the end) contains data on the median incomes (medinc) of census dissemination areas in Toronto.
(a) Treating this set of data as the population, use Minitab to calculate the population mean for the medinc variable. Set aside all population information until part (d).
(b) Now use Minitab (Calc Menu – Random Data – Sample from Columns) to draw twenty samples of size n = 40 from the Toronto medinc population. This procedure must be replicated twenty times (note that if you open up the same sampling dialog box each time from the menu, then you only have to replace the last destination column with the next one). For each sample, use Minitab to calculate a 95% confidence interval estimate for the population mean, assuming you do not know the population standard deviation (this interval estimation can be done in one operation on all twenty columns, but not in Minitab Express).
(c) For your first sample, confirm the Minitab generated interval by calculating the interval manually using the summary statistics from Minitab. Display the sample data using a boxplot and comment on whether the relevant assumption regarding the population distribution is warranted given your sample (state clearly the assumption needed to justify the interval estimation).
(d) Count the number of intervals out of your twenty that cover the true value of the population mean from part (a).
medinc
29242
22430
22398
21407
19740
24339
24953
11794
16946
22477
18274
23819
21391
14275
16307
24265
18177
21981
14081
30102
27640
34335
21458
15409
29322
20491
16986
20177
18612
23413
17190
22777
22597
19969
23229
22017
16678
18491
20013
22819
26948
18085
16750
21143
22716
25357
27489
19623
19632
22796
23230
23415
20699
28092
23339
28529
31358
21768
29246
33577
47166
36366
46652
34623
30152
26324
24934
27728
23092
38063
30356
31088
33390
23080
39173
26054
33114
31228
28941
31535
33190
28824
30191
23399
14441
26756
26229
36183
31407
24482
28228
34734
37905
53770
58328
38878
30601
36748
22083
22899
32504
20574
27468
26119
28553
23606
34628
21429
22090
21101
25053
19923
17324
18047
17525
24282
24709
21234
20589
21533
21276
24427
18520
16580
21263
15515
22370
21260
24724
22117
23375
25579
26336
18096
17400
18694
22591
23146
19951
20931
31413
32199
23981
20936
16826
20704
51411
17394
26821
19128
21323
22430
24762
23632
18588
28017
18857
18735
19513
19173
22286
22640
16152
31363
20639
17418
23429
18775
19218
26754
25940
20972
17358
20496
15921
23584
26280
19367
14644
16961
15545
18360
14305
15524
18654
11836
17261
19582
18184
26957
18771
28257
19244
25899
23819
20022
25566
19304
28794
20039
16793
31029
32356
35158
25216
19595
25482
18343
23621
17554
25560
9647
35679
27521
12579
11508
16068
16044
14327
18887
19343
10612
15435
13490
14058
22703
15533
21418
17441
15040
20017
21366
24622
27176
17202
26983
18227
40010
18741
18005
13886
10085
13910
14837
15432
18659
23188
16638
18923
50012
51397
24949
23742
51951
28220
16986
37006
34805
51036
42015
11040
15454
28269
15833
11792
27648
32676
22645
10931
8332
13372
11875
26829
34883
48469
45115
38620
56892
57993
26900
33255
27701
14334
17345
15389
29472
25565
55712
43828
60798
47892
69929
64658
34862
40763
62829
73435
30856
36062
24237
40251
31553
29869
42572
55973
31025
21610
55977
38553
25271
28967
22419
15913
28011
31163
32495
29987
19383
31049
18537
19333
26560
33696
34197
27344
21778
28160
36682
39952
36297
39776
30052
18924
15019
15616
20560
21991
33854
16763
26389
14599
23652
23188
27693
21094
14090
19976
16297
27833
13854
24717
21173
24073
20579
41419
36130
41735
35951
47018
38755
28573
33532
19008
30927
34078
36592
38934
40052
50396
37194
45892
41114
49666
32413
13419
45871
47688
53612
35415
17404
33519
46517
36008
35867
27484
44499
29156
31424
23681
41441
27635
39235
23676
24527
19483
16081
11275
37109
36889
22811
39506
30009
26271
28752
34598
28074
24757
20675
45627
23435
27351
38519
37659
45915
22765
38193
20066
28859
25029
34305
25231
25501
23253
35517
52188
25622
18829
34027
35239
29872
25947
42115
33804
26326
32654
27981
31256
21521
31676
25566
38927
30424
32447
35705
15439
17292
20780
16348
21080
23315
22854
27583
35050
37577
27931
33210
28875
39975
27605
26758
22608
21351
24025
26216
25997
29776
30761
34028
25588
26233
18015
22592
24797
22519
28953
13057
18992
26110
29474
22027
20970
34851
30062
25559
14880
22463
23275
30153
26499
36459
33627
34968
33838
19689
20314
20811
32215
25387
31606
31198
30347
20494
15669
35866
32459
29330
23444
37046
33967
24443
37708
25841
26134
23572
22738
20023
22529
21902
23950
20715
18353
26601
24869
17294
32242
19025
22226
13563
25722
23155
28741
28639
17617
25976
19562
21382
28330
35199
44126
21575
19307
21169
23735
18891
35141
21714
30527
27930
23665
19798
15146
31684
40692
35360
15006
37467
52768
38960
29816
42012
24748
31140
38118
43744
32749
22320
37307
23938
24340
33524
52737
49841
38585
38764
52260
48469
58310
36266
37598
54420
26938
30048
28960
15759
24386
35642
39940
24958
22468
24586
26842
45343
38084
28973
39252
13106
34730
21564
33336
16602
30546
40209
33989
40801
36643
24554
29220
26526
18934
13910
32513
16218
25784
22829
17412
20190
17296
22932
18999
32112
18525
22718
23167
19185
19458
25110
22282
22300
23606
15592
24690
30266
28677
32708
18742
23244
34076
27686
29932
21562
24367
17728
48076
26818
52354
18678
14696
20961
23221
35430
29637
24130
25779
24040
19220
21961
28366
23235
19423
27079
45669
31970
16440
23012
12796
19604
24508
19889
22387
25227
18393
23239
18047
21098
24231
22691
24572
21044
18218
21714
18399
18333
17159
13831
25749
27339
18430
28735
17447
18245
19337
21615
16695
17014
12899
25995
28729
15025
17072
20321
20019
28505
20762
30523
35566
26719
35795
23419
15141
26894
25867
17225
19383
18183
15658
19549
18515
17130
23411
20032
22582
20165
24682
14808
19642
23438
25772
16954
19031
20425
12519
15603
16023
20575
19143
17456
15341
16408
17807
23623
30620
21575
25104
15400
20504
16475
14046
14694
19161
24650
17282
20032
23444
20063
25414
13865
21359
14036
16506
15738
17450
17478
11569
19159
18262
23846
14838
26102
16887
23446
17429
13780
16603
15060
14397
14367
19541
20621
18293
16264
17476
18960
22544
16181
17155
18195
15831
17094
14317
14851
14335
24161
13873
16577
16901
17384
14854
20815
21427
22383
21067
29917
24152
20252
19357
15470
19969
23765
22773
11839
17466
22379
17858
24320
15761
24168
25003
25770
18174
20120
26971
16846
20256
21434
22570
25016
30337
22004
20715
33561
20981
18849
23789
18106
20598
21540
13834
21092
19238
17629
16556
20999
14898
18137
28704
15707
20810
24186
24544
Explanation / Answer
Minitab Output
Descriptive Statistics: C1
Variable Mean
C1 25614
MTB > Sample 40 C1 C2.
MTB > OneT C2;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C2
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C2 40 25587 9968 1576 (22398, 28775) -0.02 0.986
Boxplot of C2
MTB > Sample 40 C1 C3.
MTB > OneT C3;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C3
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C3 40 26412 10696 1691 (22992, 29833) 0.47 0.640
Boxplot of C3
MTB > Sample 40 C1 C4.
MTB > OneT C4;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C4
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C4 40 26176 9166 1449 (23244, 29107) 0.39 0.701
Boxplot of C4
MTB > Sample 40 C1 C5.
MTB > OneT C5;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C5
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C5 40 27276 10594 1675 (23888, 30664) 0.99 0.327
Boxplot of C5
MTB > Sample 40 C1 C6.
MTB > OneT C6;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C6
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C6 40 27376 9304 1471 (24400, 30351) 1.20 0.238
Boxplot of C6
MTB > Sample 40 C1 C7.
MTB > OneT C7;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C7
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C7 40 24209 8102 1281 (21618, 26800) -1.10 0.280
Boxplot of C7
MTB > Sample 40 C1 C8.
MTB > OneT C8;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C8
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C8 40 26242 7734 1223 (23768, 28715) 0.51 0.611
Boxplot of C8
MTB > Sample 40 C1 C9.
MTB > OneT C9;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C9
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C9 40 23506 6711 1061 (21360, 25653) -1.99 0.054
Boxplot of C9
MTB > Sample 40 C1 C10.
MTB > OneT C10;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C10
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C10 40 26679 8355 1321 (24008, 29351) 0.81 0.425
Boxplot of C10
MTB > Sample 40 C1 C11.
MTB > OneT C11;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C11
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C11 40 26060 10273 1624 (22774, 29345) 0.27 0.785
Boxplot of C11
MTB > Sample 40 C1 C12.
MTB > OneT C12;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C12
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C12 40 26313 8941 1414 (23453, 29172) 0.49 0.624
Boxplot of C12
MTB > Sample 40 C1 C13.
MTB > OneT C13;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C13
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C13 40 25911 10986 1737 (22397, 29424) 0.17 0.865
Boxplot of C13
MTB > Sample 40 C1 C14.
MTB > OneT C14;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C14
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C14 40 27136 9931 1570 (23960, 30312) 0.97 0.338
Boxplot of C14
MTB > Sample 40 C1 C15.
MTB > OneT C15;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C15
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C15 40 25832 10493 1659 (22476, 29188) 0.13 0.896
Boxplot of C15
MTB > Sample 40 C1 C16.
MTB > OneT C15;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C15
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C15 40 25832 10493 1659 (22476, 29188) 0.13 0.896
Boxplot of C15
MTB > Sample 40 C1 C17.
MTB > OneT C16;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C16
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C16 40 24626 6848 1083 (22436, 26816) -0.91 0.367
Boxplot of C16
MTB > OneT C17;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C17
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C17 40 25146 9168 1450 (22214, 28078) -0.32 0.749
Boxplot of C17
MTB > Sample 40 C1 C18.
MTB > OneT C18;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C18
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C18 40 24596 8464 1338 (21889, 27303) -0.76 0.451
Boxplot of C18
MTB > Sample 40 C1 C19.
MTB > OneT C19;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C19
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C19 40 23842 8439 1334 (21143, 26541) -1.33 0.192
Boxplot of C19
MTB > Sample 40 C1 C20.
MTB > OneT C20;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C20
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C20 40 29848 12151 1921 (25962, 33734) 2.20 0.034
Boxplot of C20
MTB > Sample 40 C1 C21.
MTB > OneT C21;
SUBC> Test 25614;
SUBC> Confidence 95.0;
SUBC> Alternative 0;
SUBC> GBoxplot.
One-Sample T: C21
Test of = 25614 vs 25614
Variable N Mean StDev SE Mean 95% CI T P
C21 40 25397 8940 1414 (22538, 28256) -0.15 0.879
Boxplot of C21
c)assumption needed to justify the interval estimation is,
We donot know population standard deviation therefore we use one sample T test for interval estimation.
d)All 20 intervals cover the true value of the population mean = 25614
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