Two object detection software programs are compared with each other in terms of object detection durations for 7 randomly selected images. Object detection, in miliseconds, for the two programs are listed below. Please consider that the two population distributions are normally distributed. Based on the information given, please find out whether there is a siqnificant difference between these two programs. Image No Image #1 Image #2 Image #3 Image #4 Program A Program B (a) State the null hypothesis to be tested and the alternative hypothesis Ho: H 470 400 530 500 680 700 500 520 (b) Conduct a statistical test of the null hypothesis and state your conclusion. Test at a = 0.05 Image #5 740 700 Image #6 Image #7 650 620 Test Statistic = 650 690 (c) Find the Critical Value(s). (d) Conclusion and interpretation: (e) Find the approximate p-value.
Two object detection software programs are compared with each other in terms of object detection durations for 7 randomly selected images. Object detection, in miliseconds, for the two programs are listed below. Please consider that the two population distributions are normally distributed. Based on the information given, please find out whether there is a siqnificant difference between these two programs. Image No Image #1 Image #2 Image #3 Image #4 Program A Program B (a) State the null hypothesis to be tested and the alternative hypothesis Ho: H 470 400 530 500 680 700 500 520 (b) Conduct a statistical test of the null hypothesis and state your conclusion. Test at a = 0.05 Image #5 740 700 Image #6 Image #7 650 620 Test Statistic = 650 690 (c) Find the Critical Value(s). (d) Conclusion and interpretation: (e) Find the approximate p-value.
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Transcribed Image Text:Two object detection software programs are compared with each other in terms of object detection durations for 7
randomly selected images. Object detection, in miliseconds, for the two programs are listed below. Please consider
that the two population distributions are normally distributed. Based on the information given, please find out whether
there is a siqnificant difference between these two programs.
Image No
Image #1
Image #2
Image #3
Image #4
Image #5
Image #6
Image #7
Program A
Program B
400
(a) State the null hypothesis to be tested and the alternative
hypothesis
Ho:
470
530
500
680
700
500
520
(b) Conduct a statistical test of the null hypothesis and state your
conclusion. Test at a = 0.05
740
700
650
620
Test Statistic =
690
650
(c) Find the Critical Value(s).
(d) Conclusion and interpretation:
(e) Find the approximate p-value.
Transcribed Image Text:TABLE D
t distribution critical values
Upper-tail probability p
df
.25
.20
.15
.10
.05
.025
.02
.01
.005
.0025
.001
.0005
1.376
1.061
0.978
15.89
4.849
3.482
2.999
636.6
31.60
1.000
1.963
3.078
12.71
6.314
2.920
2.353
31.82
63.66
127.3
318 3
22.33
10.21
7.173
5.893
5.208
0.816
0.765
1.386
1.250
1.886
1.638
1.533
1.476
1.440
4.303
3.182
2
9.925
6.965
4.541
14.09
7.453
3
5.841
12.92
0.741
0.727
0.718
0.711
0.706
0.941
0.920
0.906
1.190
1.156
1.134
2.132
2.015
3.747
3.365
3.143
4.604
4.032
3.707
8.610
6.869
5.959
4
2.776
5.598
2.571
2.447
2.365
2.306
2.757
2.612
2.517
2.449
2.398
2.359
2.328
4.773
4.317
6.
1.943
0.896
0.889
2.998
2.896
1.119
1.108
1.100
1.093
1088
7
8
1.415
1.397
1.895
1.860
3.499
3.355
4.029
3.833
4.785
4.501
5.408
5.041
0.703
0.700
0.883
0.879
0.876
1.833
1.812
1.796
2.821
2.764
3.250
3.169
4.297
4.144
9.
1.383
1.372
1.363
2.262
2.228
3.690
3.581
4.781
4.587
10
11
0.697
2.201
2.718
3.106
3.497
4.025
4.437
df
X.990
X.050
2
X900
X,100
X050
X010
X.005
0.000
0.000
0.001
0.004
0.016
2.706
3.841
5.024
6.635
7.879
0.010
0.020
0.051
0.103
0.211
4.605
5.991
7.378
9.210
10.597
Chi-Square Distribution Ta.
3
0.072
0.115
0.216
0.352
0.584
6.251
7.815
9.348
11.345
12.838
0.207
0.297
1.064
0.484
0.831
0.711
7.779
9.488
11.143
13.277
14.860
16.750
18.548
0.412
0.554
1.145
1.610
9.236
11.070
12.833
15.086
6.
0,676
0.872
1.237
1.635
2.204
10.645
12.592
14.449
16.812
0.989
1.239
1.690
2.167
2.833
12.017
14.067
16.013
18.475
20.278
1.344
1.646
2.180
2.733
3.490
13.362
15.507
17.535
20.090
21.955
1.735
2.088
2.700
3.325
4.168
14.684
16.919
19.023
21.666
23.589
2.156
2.558
3.247
3.940
4.865
15.987
18.307
20.483
23.209
25.188
The shaded avn is equal to o for -
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