Problem 4: A machine is used to fill containers with a liquid product. Fill volume can be assumed to be normally distributed. A random sample of ten
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Problem 4: A machine is used to fill containers with a liquid product. Fill volume can be assumed
to be normally distributed. A random sample of ten containers is selected, and the net contents
(02) are as follows: 1203,1201, 1204,1202, 12.06, 11.98, 11.97, 12.02, 12.05 and 11.99. (a) Suppose that the manufacturer wants to be sure that the mean net contents exceeds 12 02.
What conclusions can be drawn from the data, based on typel error =0.01. (b) What is the P-value for this test?
(c) Discuss why a one—sided alternative was chosen in part (a). (d) Construct a 99% two-sided confidence interval on the mean containers.

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Appendix
APPENDIX IV
Percentage Points of the t Distribution
av
0.40
0.25
0.025
0.01
0.005
0.0025
0.001
0.0005
0.325
1.000
3.078
6.314
12.706
63.657
127.32
318.31
0.289
0.816
1.886
2.920
4.303
6.965
9.925
14.089
23.326
31.598
0.765
1.638
2.353
3.182
4.541
5.841
12.924
0.271
0.741
1.533
2.132
2.776
3.747
4.604
5.598
7.173
8.610
1.476
2.571
4.032
4.773
5.893
6.869
0.727
1.440
1.943
2.447
3.143
3.707
4.317
5.208
5.959
0.711
1.415
1.895
2.365
2.998
5.408
0.706
2.306
2.896
3.355
3.833
4.501
5.041
0.703
1.383
1.833
2.262
2.821
3.250
3.690
4.297
4.781
10 0.260
0.700
1.372
1.812
2.228
2.764
3.581
4.144
4.587
11 0.260
0.697
1.363
1.796
2.20
3.106
4.025
4.437
12 0.259
0.695
1.782
2.179
2.681
3.055
3.428
3.930
4.318
0.694
1.350
2.160
2.650
3.012
3.372
3.852
14 0.258
0.692
1.345
1.761
2.145
2.624
2.977
15 0.258
3.326
3.787
4.140
0.691
2.131
2.947
3.286
16 0.258
4.073
0.690
1.337
1.746
2.120
2.583
2.921
3.252
3.686
4.015
1.333
2.110
2.898
3.222
3.646
18 0.257
3.965
0.688
1.330
1.734
2.101
2.552
2.878
3.197
19 0.257
3.610
3.992
0.688
1.328
2.093
2.539
2.861
3.174
20 0.257
3.579
3.883
0.687
1.325
1.725
2.086
2.528
2.845
3.153
0.686
3.552
3.850
1.721
2.080
2.518
2.831
3.135
22 0.256
3.527
3.819
0.686
1.321
1.717
2.074
2.508
2.819
3.119
23 0.256
3.505
3.792
0.685
1.319
2.069
2.500
2.807
3.104
24 0.256
3.485
3.767
0.685
1.711
2.064
2.492
2.797
0.684
3.467
3.745
2.060
2.485
2.787
3.078
26 0.256
3.450
3.725
0.684
1.315
1.706
2.056
2.479
2.779
3.067
27 0.256
3.435
3.707
0.684
1.703
2.052
2.473
2.771
3.057
3.421
3.690
0.683
1.313
1.701
2.048
2.763
3.047
3.408
0.683
3.674
1.311
1.699
2.045
2.462
2.756
3.038
3.396
30 0.256
3.659
0.683
1.697
2.042
2.457
2.750
3.030
3.385
3.646
0.681
1.684
2.021
2.423
2.704
2.971
3.307
3.551
1.296
1.671
2.000
2.660
2.915
120 0.254
3.232
3.460
0.677
1.289
1.658
1.980
2.358
2.617
2.860
3.160
3.373
0.253
1.282
1.645
1.960
3.090
3.291
v = degrees of freedom
Source: Adapted with permission from Biometrika Tables for Statisticians, Vol. 1, 3rd ed., by E. S. Pearson and H. O. Hartley,
Cambridge University Press, Cambridge, 1966.

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