(a) Make a stemplot. Are there outliers or strong skewness that would forbid use of the i procedures? O The stemplot suggests the presence of outliers. The sample is small and the stemplot skewed, so the use of r not appropriate. procedures O The stemplot suggests the presence procedures is appropriate. O The stemplot does not indicate the presence of outliers. The sample is small but the stemplot is not skewed, so the outliers. The sample is small but the stemplot is not skewed, so the use of t use of t procedures is appropriate. O The stemplot does not indicate the presence of outliers. The sample is small and the stemplot of t procedures is not appropriate. skewed, so the use (b) A good way to judge the effect of outliers is to do your analysis twice, once with the outliers and a second time without them. Give two 90% confidence intervals, one with all the data and one with the outliers removed, for the mean pollution intake among all school buses used in the Southern California Air Basin that travel the route investigated in the study. Use Table Cor the software of your choice for these calculations. (Enter your answers rounded to three decimal places.) lower bound an data = (c) Compare the two intervals in part (b). What is the most important effect of removing the outliers? upper bound ta = O increasing of confidence interval O reducing margins of error lower bound outlien remned= O reducing of confidence interval O simplification of calculations upper boundutliers remened =

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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In a study of exhaust emissions from school buses, the pollution intake by passengers was determined for a sample of
nine school buses used in the Southern California Air Basin. The pollution intake is the amount of exhaust emissions, in
grams per person, that would be inhaled while traveling on the bus during its usual 18-mile trip on congested freeways
from South Central LA to a magnet school in West LA. (As a reference, the average intake of motor emissions of carbon
monoxide in the LA area is estimated to be about 0.000046 grams per person.) The amounts for the nine buses when
driven with the windows open are given.
1.15
0.33
0.40
0.33
1.35
0.38
0.25
0.40
0.35
(a) Make a stemplot. Are there outliers or strong skewness that would forbid use of the t procedures?
The stemplot suggests the presence of outliers. The sample is small and the stemplot is skewed, so the use of t
procedures is not appropriate.
The stemplot suggests the presence of outliers. The sample is small but the stemplot is not skewed, so the use of t
procedures is appropriate.
The stemplot does not indicate the presence of outliers. The sample is small but the stemplot is not skewed, so the
use of t procedures is appropriate.
The stemplot does not indicate the presence of outliers. The sample is small and the stemplot is skewed, so the use
of t procedures is not appropriate.
(b) A good way to judge the effect of outliers is to do your analysis twice, once with the outliers and a second time
without them. Give two 90% confidence intervals, one with all the data and one with the outliers removed, for the mean
pollution intake among all school buses used in the Southern California Air Basin that travel the route investigated in the
study. Use Table C or the software of your choice for these calculations. (Enter your answers rounded to three decimal
places.)
lower bound all data
(c) Compare the two intervals in part (b). What is the most important effect of removing the outliers?
upper bound
O increasing of confidence interval
%3D
all data
reducing margins of error
lower bound outliers removed =
reducing of confidence interval
O simplification of calculations
upper bound outliers removed
Transcribed Image Text:In a study of exhaust emissions from school buses, the pollution intake by passengers was determined for a sample of nine school buses used in the Southern California Air Basin. The pollution intake is the amount of exhaust emissions, in grams per person, that would be inhaled while traveling on the bus during its usual 18-mile trip on congested freeways from South Central LA to a magnet school in West LA. (As a reference, the average intake of motor emissions of carbon monoxide in the LA area is estimated to be about 0.000046 grams per person.) The amounts for the nine buses when driven with the windows open are given. 1.15 0.33 0.40 0.33 1.35 0.38 0.25 0.40 0.35 (a) Make a stemplot. Are there outliers or strong skewness that would forbid use of the t procedures? The stemplot suggests the presence of outliers. The sample is small and the stemplot is skewed, so the use of t procedures is not appropriate. The stemplot suggests the presence of outliers. The sample is small but the stemplot is not skewed, so the use of t procedures is appropriate. The stemplot does not indicate the presence of outliers. The sample is small but the stemplot is not skewed, so the use of t procedures is appropriate. The stemplot does not indicate the presence of outliers. The sample is small and the stemplot is skewed, so the use of t procedures is not appropriate. (b) A good way to judge the effect of outliers is to do your analysis twice, once with the outliers and a second time without them. Give two 90% confidence intervals, one with all the data and one with the outliers removed, for the mean pollution intake among all school buses used in the Southern California Air Basin that travel the route investigated in the study. Use Table C or the software of your choice for these calculations. (Enter your answers rounded to three decimal places.) lower bound all data (c) Compare the two intervals in part (b). What is the most important effect of removing the outliers? upper bound O increasing of confidence interval %3D all data reducing margins of error lower bound outliers removed = reducing of confidence interval O simplification of calculations upper bound outliers removed
TABLES
699
Table entry for C is the critical value
t* required for confidence level C.
To approximate one- and two-sided
P-values, compare the value of the t
Tail area
statistic with the critical values of t*
Area C
that match the P-values given at the
bottom of the table.
t*
TABLE C t distribution critical values
Confidence level C
Degrees of
freedom
50%
60%
70%
80%
90%
95%
96%
98%
99%
99.5%
99.8%
99.9%
1
1.000
1.376
1.963
3.078
6.314
12.71
15.89
31.82
63.66
127.3
318.3
636.6
0.816
1.061
1.386
1.886
2.920
4.303
4.849
6.965
9.925
14.09
22.33
31.60
1.250
7.453
5.598
3
0.765
0.978
1.638
2.353
3.182
3.482
4.541
5.841
10.21
12.92
4
0.741
0.941
1.190
1.533
2.132
2.776
2.999
3.747
4.604
7.173
8.610
0.727
0.920
1.156
1.476
2.015
2.571
2.757
3.365
4.032
4.773
5.893
6.869
6.
0.718
0.906
1.134
1.440
1.943
2.447
2.612
3.143
3.707
5.208
4.317
4.029
5.959
7
0.711
0.896
1.119
1.415
1.895
2.365
2.517
2.998
3.499
4.785
5.408
8
0.706
0.889
1.108
1.397
1.860
2.306
2.449
2.896
3.355
3.833
4.501
5.041
9.
0.703
0.883
1.100
1.383
1.833
2.262
2.398
2.821
3.250
3.690
4.297
4.781
10
0.700
0.879
1.093
1.372
1.812
2.228
2.359
2.764
3.169
3.581
4.144
4.587
11
0.697
0.876
1.088
1.363
1.796
2.201
2.328
2.718
3.106
3.497
4.025
4.437
12
0.695
0.873
1.083
1.356
1.782
2.179
2.303
2.681
3.055
3.428
3.930
4.318
13
0.694
0.870
1.079
1.350
1.771
2.160
2.282
2.650
3.012
3.372
3.852
4.221
14
0.692
0.868
1.076
1.345
1.761
2.145
2.264
2.624
2.977
3.326
3.787
4.140
15
0.691
0.866
1.074
1.341
1.753
2.131
2.249
2.602
2.947
3.286
3.733
4.073
16
0.690
0.865
1.071
1.337
1.746
2.120
2.235
2.583
2.921
3.252
3.686
4.015
17
0.689
0.863
1.069
1.333
1.740
2.110
2.224
2.567
2.898
3.222
3.646
3.965
18
0.688
0.862
1.067
1.330
1.734
2.101
2.214
2.552
2.878
3.197
3.611
3.922
1.066
1.064
1.729
1.725
19
0.688
0.861
1.328
2.093
2.205
2.539
2.861
3.174
3.579
3.883
20
0.687
0.860
1.325
2.086
2.197
2.528
2.845
3.153
3.552
3.850
1.063
1.323
3.135
3.527
3.505
21
0.686
0.859
1.721
2.080
2.189
2.518
2.831
3.819
0.858
0.858
22
0.686
1.061
1.321
1.717
2.074
2.183
2.508
2.819
3.119
3.792
23
0.685
1.060
1.319
3.485
1.714
1.711
2.069
2.177
2.500
2.807
3.104
3.768
24
0.685
0.857
1.059
1.318
2.064
2.172
2.492
2.797
3.091
3.467
3.745
25
0.684
0.856
1.058
1.316
1.708
2.060
2.167
2.485
2.787
3.078
3.450
3.725
26
0.684
0.856
1.058
1.315
1.706
2.056
2.162
2.479
2.779
3.067
3.435
3.707
27
0.684
0.855
1.057
1.314
1.703
2.052
2.158
2.473
2.771
3.057
3.421
3.690
28
0.683
0.855
1.056
1.313
1.701
2.048
2.154
2.467
2.763
3.047
3.408
3.674
29
0.683
0.854
1.055
1.311
1.699
2.045
2.150
2.462
2.756
3.038
3.396
3.659
30
0.683
0.854
1.055
1.310
1.697
2.042
2.147
2.457
2.750
3.030
3.385
3.646
40
0.681
0.851
1.050
1.303
1.684
2.021
2.123
2.423
2.704
2.971
3.307
3.551
0.679
0.679
50
0.849
1.047
1.299
1.676
2.009
2.109
2.403
2.678
2.937
3.261
3.496
60
0.848
1.045
1.296
1.671
2.000
2.099
2.390
2.660
2.915
3.232
3.460
80
0.678
0.846
1.043
1.292
1.664
1.990
2.088
2.374
2.639
2.887
3.195
3.416
100
0.677
0.845
1.042
1.290
1.660
1.984
2.081
2.364
2.626
2.871
3.174
3.390
1000
0.675
0.842
1.037
1.282
1.646
1.962
2.056
2.330
2.581
2.813
3.098
3.300
0.674
0.841
1.036
1.282
1.645
1.960
2.054
2.326
2.576
2.807
3.091
3.291
One-sided P
.25
.20
.15
.10
.05
.025
.02
.01
.005
.0025
.001
.0005
Two-sided P
.50
.40
.30
.20
.10
.05
.04
.02
.01
.005
.002
.001
Transcribed Image Text:TABLES 699 Table entry for C is the critical value t* required for confidence level C. To approximate one- and two-sided P-values, compare the value of the t Tail area statistic with the critical values of t* Area C that match the P-values given at the bottom of the table. t* TABLE C t distribution critical values Confidence level C Degrees of freedom 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 1 1.000 1.376 1.963 3.078 6.314 12.71 15.89 31.82 63.66 127.3 318.3 636.6 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.09 22.33 31.60 1.250 7.453 5.598 3 0.765 0.978 1.638 2.353 3.182 3.482 4.541 5.841 10.21 12.92 4 0.741 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 7.173 8.610 0.727 0.920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 6. 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 5.208 4.317 4.029 5.959 7 0.711 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.785 5.408 8 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 9. 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 11 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437 12 0.695 0.873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 14 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 15 0.691 0.866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 16 0.690 0.865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 17 0.689 0.863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 18 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.611 3.922 1.066 1.064 1.729 1.725 19 0.688 0.861 1.328 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 0.687 0.860 1.325 2.086 2.197 2.528 2.845 3.153 3.552 3.850 1.063 1.323 3.135 3.527 3.505 21 0.686 0.859 1.721 2.080 2.189 2.518 2.831 3.819 0.858 0.858 22 0.686 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.792 23 0.685 1.060 1.319 3.485 1.714 1.711 2.069 2.177 2.500 2.807 3.104 3.768 24 0.685 0.857 1.059 1.318 2.064 2.172 2.492 2.797 3.091 3.467 3.745 25 0.684 0.856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 26 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 27 0.684 0.855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 3.690 28 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674 29 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659 30 0.683 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 40 0.681 0.851 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 0.679 0.679 50 0.849 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 60 0.848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 80 0.678 0.846 1.043 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195 3.416 100 0.677 0.845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174 3.390 1000 0.675 0.842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098 3.300 0.674 0.841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291 One-sided P .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 Two-sided P .50 .40 .30 .20 .10 .05 .04 .02 .01 .005 .002 .001
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