Critical Values of the t-Distribution 0.40 0.30 0.20 0.15 0.10 0.05 0.025 0.325 0.727 0.617 1.376 1.963 1.386 1.250 1.190 1 3.078 6.314 12.706 0.289 0.277 0.271 2 1.061 1.886 2.920 4.303 1.638 1.533 1.476 3 0.584 0.978 2.353 3.182 0.569 0.941 2.132 2.776 5 0.267 0.559 0.920 1.156 2.015 2.571 6 0.265 0.553 0.906 1.134 1.440 1.943 2.447 0.263 0.262 0.896 0.889 0.883 0.879 2.365 2.306 7 0.549 1.119 1.415 1.895 1.108 1.100 8 0.546 1.397 1.860 0.543 0.542 1.833 1.812 0.261 1.383 2.262 2.228 10 0.260 1.093 1.372 0.260 0.259 1.796 1.782 2.201 0.876 0.873 1.088 1.083 1.363 1.356 11 0.540 12 0.539 0.538 2.179 0.259 0.258 0.258 13 0.870 1.079 1.350 1.771 2.160 2.145 2.131 0.537 0.868 1.076 1.074 1.345 1.341 14 1.761 15 0.536 0.866 1.753 0.258 0.257 0.257 0.257 0.865 0.863 0.862 1.071 1.069 1.067 1.337 1.333 1.330 16 0.535 1.746 2.120 17 0.534 1.740 2.110 0.534 2.101 2.093 18 1.734 1.066 1.064 1.328 1.325 1.729 1.725 19 0.533 0.861 20 0.257 0.533 0.860 2.086

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Critical Values of the t-Distribution
0.40
0.30
0.20
0.15
0.10
0.05
0.025
0.325
0.727
0.617
1.376
1.963
1.386
1.250
1.190
1
3.078
6.314
12.706
4.303
3.182
0.289
1.061
1.886
2.920
1.638
1.533
3
0.277
0.584
0.978
2.353
0.569
0.559
0.941
0.920
0.271
2.132
2.776
5.
0.267
1.156
1.476
2.015
2.571
0.265
0.263
0.262
0.906
0.896
0.889
1.134
1.943
1.895
2.447
2.365
2.306
0.553
1.440
7
0.549
1.119
1.415
8
0.546
1.108
1.397
1.860
0.543
0.542
0.883
1.833
1.812
0.261
1.100
1.383
2.262
10
0.260
0.879
1.093
1.372
2.228
0.260
0.259
0.259
0.258
0.876
0.873
1.363
1.356
1.796
1.782
2.201
2.179
2.160
2.145
11
0.540
1.088
12
0.539
1.083
13
0.538
0.870
1.079
1.350
1.771
0.537
0.868
1.076
1.345
1.341
14
1.761
15
0.258
0.536
0.866
1.074
1.753
2.131
0.535
0.534
0.865
0.863
0.862
16
0.258
1.071
1.337
1.746
2.120
1.333
1.330
17
0.257
1.069
1.740
2.110
1.067
1.066
1.064
1.734
1.729
1.725
18
0.257
0.257
0.257
0.534
2.101
0.861
0.860
1.328
1.325
2.093
0.533
0.533
19
20
2.086
0.532
0.532
0.532
0.859
0.858
1.063
1.061
1.060
21
1.721
0.257
0.256
1.323
2.080
1.321
2.074
2.069
22
1.717
23
0.256
0.858
1.319
1.714
1.711
0.256
0.256
24
0.531
0.857
1.059
1.318
2.064
25
0.531
0.856
1.058
1.316
1.708
2.060
0.531
0.256
0.256
1.058
1.057
26
1.706
0.856
0.855
1.315
2.056
27
0.531
1.314
1.703
2.052
Print
Done
Transcribed Image Text:Critical Values of the t-Distribution 0.40 0.30 0.20 0.15 0.10 0.05 0.025 0.325 0.727 0.617 1.376 1.963 1.386 1.250 1.190 1 3.078 6.314 12.706 4.303 3.182 0.289 1.061 1.886 2.920 1.638 1.533 3 0.277 0.584 0.978 2.353 0.569 0.559 0.941 0.920 0.271 2.132 2.776 5. 0.267 1.156 1.476 2.015 2.571 0.265 0.263 0.262 0.906 0.896 0.889 1.134 1.943 1.895 2.447 2.365 2.306 0.553 1.440 7 0.549 1.119 1.415 8 0.546 1.108 1.397 1.860 0.543 0.542 0.883 1.833 1.812 0.261 1.100 1.383 2.262 10 0.260 0.879 1.093 1.372 2.228 0.260 0.259 0.259 0.258 0.876 0.873 1.363 1.356 1.796 1.782 2.201 2.179 2.160 2.145 11 0.540 1.088 12 0.539 1.083 13 0.538 0.870 1.079 1.350 1.771 0.537 0.868 1.076 1.345 1.341 14 1.761 15 0.258 0.536 0.866 1.074 1.753 2.131 0.535 0.534 0.865 0.863 0.862 16 0.258 1.071 1.337 1.746 2.120 1.333 1.330 17 0.257 1.069 1.740 2.110 1.067 1.066 1.064 1.734 1.729 1.725 18 0.257 0.257 0.257 0.534 2.101 0.861 0.860 1.328 1.325 2.093 0.533 0.533 19 20 2.086 0.532 0.532 0.532 0.859 0.858 1.063 1.061 1.060 21 1.721 0.257 0.256 1.323 2.080 1.321 2.074 2.069 22 1.717 23 0.256 0.858 1.319 1.714 1.711 0.256 0.256 24 0.531 0.857 1.059 1.318 2.064 25 0.531 0.856 1.058 1.316 1.708 2.060 0.531 0.256 0.256 1.058 1.057 26 1.706 0.856 0.855 1.315 2.056 27 0.531 1.314 1.703 2.052 Print Done
Two catalysts in a batch chemical process are being compared for their effect on the output of the process reaction. A sample of 14 batches was prepared using catalyst 1 and gave an average yield of 88 with a sample standard deviation of 5. A
sample of 10 batches was prepared using catalyst 2 and gave an average yield of 83 and a sample standard deviation of 4. Find a 90% confidence interval for the difference between the population means, assuming that the populations are
approximately normally distributed with equal variances.
Click here to view page 1 of the table of critical values of the t-distribution.
Click here to view page 2 of the table of critical values of the t-distribution.
Let
be the population mean for catalyst 1 and let µ2 be the population mean for catalyst 2.
|<H1- H2<
(Round to two decimal places as needed.)
The confidence interval is
く
Transcribed Image Text:Two catalysts in a batch chemical process are being compared for their effect on the output of the process reaction. A sample of 14 batches was prepared using catalyst 1 and gave an average yield of 88 with a sample standard deviation of 5. A sample of 10 batches was prepared using catalyst 2 and gave an average yield of 83 and a sample standard deviation of 4. Find a 90% confidence interval for the difference between the population means, assuming that the populations are approximately normally distributed with equal variances. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. Let be the population mean for catalyst 1 and let µ2 be the population mean for catalyst 2. |<H1- H2< (Round to two decimal places as needed.) The confidence interval is く
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