Quality Control of Coins: P-Value MethodRepeat Example 1 using the P-value method of testing hypotheses.
Example 1
Quality Control of Coins: Traditional MethodA common goal in business and industry is to improve the quality of goods or services by reducing variation. Quality control engineers want to ensure that a product has an acceptable mean, but they also want to produce items of consistent quality so that there will be few defects. If weights of coins have a specified mean but too much variation, some will have weights that are too low or too high, so that vending machines will not work correctly (unlike the stellar performance that they now provide). Consider the simple random sample of the 37 weights of post-1983 pennies listed in Data Set 20 in Appendix B. Those 37 weights have a mean of 2.49910 g and a standard deviation of 0.01648 g. U.S. Mint specifications require that pennies be manufactured so that the mean weight is 2.500 g. A hypothesis test will verify that the sample appears to come from a population with a mean of 2.500 g as required, but use a 0.05 significance level to test the claim that the population of weights has a standard deviation less than the specification of 0.0230 g.
Data Set 20: Coin Weights (grams)
The “pre-1983 pennies” were made after the Indian and wheat pennies, and they are 97% copper and 3% zinc. The “post-1983 pennies” are 3% copper and 97% zinc. The “pre-1964 silver quarters” are 90% silver and 10% copper. The “post-1964 quarters” are made with a copper-nickel alloy.
STATDISK:
Data set name is Coins.
Minitab:
Worksheet name is COINS.MTW.
Excel:
Workbook name is COINS.XLS.
TI-83/84 Plus:
App name is COINS, and the file names are the same as for text files.
Text file names:
Text file names are CPIND, CPWHT, CPPRE, CPPST, CPCAN, CQPRE, CQPST, CDOL.
Indian pennies
Wheat pennies
Pre-1983
Pennies
Post-1983 pennies
Canadian pennies
Pre-1964
Quarters
Post-1964
Dollar Coins
3.0630
3.1366
3.1582
2.5113
3.2214
6.2771
5.7027
8.1008
3.0487
3.0755
3.0406
2.4907
3.2326
6.2371
5.7495
8.1072
2.9149
3.1692
3.0762
2.5024
2.4662
6.1501
5.7050
8.0271
3.1358
3.0476
3.0398
2.5298
2.8357
6.0002
5.5941
8.0813
2.9753
3.1029
3.1043
2.4950
3.3189
6.1275
5.7247
8.0241
3.0377
3.1274
2.5127
3.2612
6.2151
5.6114
8.0510
3.1083
3.0775
2.4998
3.2441
6.2866
5.6160
7.9817
3.1141
3.1038
2.4848
2.4679
6.0760
5.5999
8.0954
3.0976
3.1086
2.4823
2.7202
6.1426
5.7790
8.0658
3.0862
3.0586
2.5163
2.5120
6.3415
5.6841
8.1238
3.0570
3.0603
2.5222
6.1309
5.6234
8.1281
3.0765
3.0502
2.5004
6.2412
5.5928
8.0307
3.1114
3.1028
2.5248
6.1442
5.6486
8.0719
3.0965
3.0522
2.5058
6.1073
5.6661
8.0345
3.0816
3.0546
2.4900
6.1181
5.5361
8.0775
3.0054
3.0185
2.5068
6.1352
5.5491
8.1384
3.1934
3.0712
2.5016
6.2821
5.7239
8.1041
3.1461
3.0717
2.4797
6.2647
5.6555
8.0894
2.5067
6.2908
5.6063
8.0538
3.1267
3.0817
2.5139
6.1661
5.5709
8.0342
3.1524
3.0704
2.4762
6.2674
5.5591
3.0786
3.0797
6.2718
5.5864
3.0131
3.0713
2.5170
6.1949
5.6872
3.1535
3.0631
2.4925
6.2465
5.6274
3.0480
3.0866
2.4876
6.3172
5.6157
3.0050
3.0763
2.4933
6.1487
5.6668
3.0290
3.1299
2.4806
6.0829
5.7198
3.0846
6.1423
5.6694
3.0357
3.0917
2.5017
6.1970
5.5454
3.0064
3.0877
6.2441
5.6646
3.0936
2.9593
2.4973
6.3669
5.5636
3.1031
3.0966
2.5252
6.0775
5.6485
3.0408
2.9800
2.4978
6.1095
5.6703
3.0561
3.0934
2.5073
6.1787
5.6848
3.0994
3.1340
2.4658
6.2130
5.5609
2.4529
6.1947
5.7344
2.5085
6.1940
5.6449
6.0257
5.5804
6.1719
5.6010
6.3278
5.6022
Already registered? Login
Not Account? Sign up
Enter your email address to reset your password
Back to Login? Click here