a manufacturing process that produces a critical component for an aerospace application. The reliability of this component is of utmost importance. The manufacturing team claims that the mean reliability of the components produced is 0.98. However, the quality control team is skeptical and decides to perform hypothesis testing to verify this claim. You can refer to Appendix A for Z score table. i. iv. ii. iii. State the null hypothesis and the alternative hypothesis that the quality control team should use to test the manufacturing team's claim. Explain the concept of Type I and Type II errors in the context of this hypothesis test. How might each type of error impact the assessment of the component's reliability? If a random sample of 50 components is taken, and the sample mean reliability is found to be 0.975 with a standard deviation of 0.008, conduct a hypothesis test at a significance level of 0.05. Provide the necessary calculations, state the conclusion, and interpret the results. Discuss the implications of the hypothesis test results for the manufacturing process. How might the findings influence decisions regarding product reliability and quality contro measures?
a manufacturing process that produces a critical component for an aerospace application. The reliability of this component is of utmost importance. The manufacturing team claims that the mean reliability of the components produced is 0.98. However, the quality control team is skeptical and decides to perform hypothesis testing to verify this claim. You can refer to Appendix A for Z score table. i. iv. ii. iii. State the null hypothesis and the alternative hypothesis that the quality control team should use to test the manufacturing team's claim. Explain the concept of Type I and Type II errors in the context of this hypothesis test. How might each type of error impact the assessment of the component's reliability? If a random sample of 50 components is taken, and the sample mean reliability is found to be 0.975 with a standard deviation of 0.008, conduct a hypothesis test at a significance level of 0.05. Provide the necessary calculations, state the conclusion, and interpret the results. Discuss the implications of the hypothesis test results for the manufacturing process. How might the findings influence decisions regarding product reliability and quality contro measures?
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Transcribed Image Text:(a)
Consider a manufacturing process that produces a critical component for
an aerospace application. The reliability of this component is of utmost
importance. The manufacturing team claims that the mean reliability of
the components produced is 0.98. However, the quality control team is
skeptical and decides to perform hypothesis testing to verify this claim.
You can refer to Appendix A for Z score table.
i.
iv.
ii.
iii.
State the null hypothesis and the alternative hypothesis that
the quality control team should use to test the manufacturing
team's claim.
Explain the concept of Type I and Type II errors in the
context of this hypothesis test. How might each type of error
impact the assessment of the component's reliability?
If a random sample of 50 components is taken, and the
sample mean reliability is found to be 0.975 with a standard
deviation of 0.008, conduct a hypothesis test at a significance
level of 0.05. Provide the necessary calculations, state the
conclusion, and interpret the results.
Discuss the implications of the hypothesis test results for the
manufacturing process. How might the findings influence
decisions regarding product reliability and quality control
measures?
Ensure to show all calculations and justify your answers
Transcribed Image Text:Appendix A: Negative Z Score Table
-0.9
-0.8
Z
0.06
0.01
0.00
0.00005 0.00005
-3.9
0.00004
-3.8
0.00007
0.00007
0.00006
-3.7
0.00011
0.00010
0.00008
-3.6
0.00016
0.00015 0.00015
0.00013
-3.5
0.00023
0.00022 0.00021
0.00019
-3.4
0.00034
0.00027
-3.3
0.00048
0.00045 0.00043
0.00042
0.00039
-3.2
0.00022
0.00032 0.00031 0.00030
0.00047
0.00066 0.00064 0.00062
0.00087
0.00131 0.00126 0.00122
0.00069
0.00060
0.00056
0.00094 0.00090
0.00084
0.00079
0.00118
0.00111
0.00154
-3.1
0.00097
-3.0 0.00135
-2.9 0.00187 0.00181 0.00175
-2.8 0.00256 0.00248 0.00240
-2.7 0.00347 0.00336 0.00326
-2.6 0.00466 0.00453
0.00427
0.00440
-2.5 0.00621 0.00604 0.00587 0.00570
0.00169 0.00164 0.00159
0.00233 0.00226
0.00317 0.00307
0.00219
0.00212
0.00298
0.00289
0.00415
0.00402
0.00391
0.00539
0.00554
0.00523
-2.4 0.00820
0.00798
0.00776
0.00755
0.00714
0.00695
0.00676
0.00734
0.00990 0.00964
-2.3 0.01072 0.01044
0.01017
0.00914
0.00939
0.00889
-2.2 0.01390 0.01355 0.01321 0.01287
0.01255
0.01222
0.01191
0.01160
-2.1 0.01786 0.01743 0.01700
0.01659
0.01618
0.01578
0.01539
0.01500
-2.0
0.02275 0.02222
0.02169
0.02118
0.02068 0.02018
0.01970
0.01923
-1.9
0.02872
0.02807
0.02743
0.02680
0.02619
0.02500
0.02442
0.02385
-1.8
0.03593
0.03515
0.03438
0.03144 0.03074
0.03005
-1.7
0.04457
0.04363
0.03836 0.03754
-1.6 0.05480
0.04746
0.04648
0.03362 0.03288
0.04093
0.04272 0.04182
0.05155 0.05050
0.05370 0.05262
0.06301 0.06178 0.06057
0.06681 0.06552 0.06426
0.07493 0.07353
0.07636
0.08076
0.09680
-1.5
0.05938 0.05821
0.05705
-1.4
0.07927 0.07780
0.07215 0.07078
0.06944
-1.3
0.09510
0.09342
0.09176
0.09012
0.08851
0.08691
0.08534
0.08379
-1.2 0.11507
0.11314
0.11123
0.10935
0.10749
0.10565
0.10383 0.10204
0.10027
-1.1
0.13567
0.13350
0.13136
0.12924
0.12714
0.11900
-LO
0.15866
0.15386
0.15625
0.15151
0.18406
0.18141
0.17879
0.17619
0.12507 0.12302 0.12100
0.14917 0.14686 0.14457 0.14231 0.14007
0.17361 0.17106 0.16853 0.16602 0.16354
0.19489
0.22363
0.25785 0.25463
021186
0.20611
0.20897
0.20327
0.20045
0.19766
0.19215 0.18943
0.24196
0.23885
0.23576
0.23270
0.22965
0.22663
0.22065 0.21770
027425
0.27093
0.26763
0.26435
0.26109
0.30854
0.30503
0.30153 0.29806
0.34458 0.34090
0.25143
0.29116 0.28774 0.28434
0.32636 0.32276 031918 031561
0.37828
0.38209
0.36317 0.35942 0.35569 0.35197
0.42074 0.41683
0.40905 0.40517 0.40129 0.39743 0.39358 0.38974
-0.1 0.46017 0.45620 0.45224 0.44828 0.44433 0.44038 0.43644 0.43251 0.42858
0.0 0.50000 0.49601 0.49202 0.48803 0.48405 0.48006 0.47608 0.47210 0.46812
0.29460
0.33724 0.33360 0.32997
0.37448 0.37070 0.36693
0.41294
-0.3
-0.2
-0.7
-0.6
-0.5
-0.4
0.08
0.00003
0.00005
0.00008
0.00012
0.00017
0.00025
0.00036
0.00052
0.00074
0.00107 0.00104
0.02
0.03
0.04
0.05
0.00004 0.00004
0.00004
0.00004
0.00007 0.00006 0.00006
0.00006
0.00009
0.00009
0.00010 0.00010
0.00014
0.00014 0.00013
0.00020 0.00019
0.00029
0.00028
0.00040
0.00058
0.00082
0.00114
0.07
0.00004
0.00005
0.00008
0.00012
0.00018
0.00026
0.00038
0.00054
0.00076
0.00149 0.00144
0.00205
0.00199
0.00280
0.00272
0.003.79
0.00368
0.00508 0.00494
0.00657
0.00866
0.02559
0.03216
0.03920
0.04006
0.04846
0.04947
0.01130
0.01463
0.01876
0.09
0.00003
0.00005
0.00008
0.00011
0.00017
0.00024
0.00035
0.00050
0.00071
0.00100
0.00139
0.00193
0.00264
0.00357
0.00480
0.00639
0.00842
0.01101
0.01426
0.01831
0.02330
0.02938
0.03673
0.04551
0.05592
0.06811
0.08226
0.09853
0.11702
0.13786
0.16109
0.18673
0.21476
0.24510
0.24825
0.28096 0.27760
031207
0.34827
0.38591
0.42465
0.46414
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