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Calculate the critical sample mean Xα , the ZX̅α , The probability of type II error β and the power of the hypothesis test P. Solution: [Write the rules/formula] Calculate X̅α : Calculate ZX̅α with the true mean μ = 53: The probability of type II error β: The power of the hypothesis test P:

Calculate the critical sample mean Xα , the ZX̅α , The probability of type II error β and the power of the hypothesis test P. Solution: [Write the rules/formula] Calculate X̅α : Calculate ZX̅α with the true mean μ = 53: The probability of type II error β: The power of the hypothesis test P:

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter84: Binary Numeration System
Section: Chapter Questions
Problem 10A: Analyze the following numbers. 0.802
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Suppose we fail to reject Ho: μ ≥ 50 When the true mean is μ = 53
Given a sample of size n=64 and σ =6 and with α=0.05
Calculate the critical sample mean Xα , the ZX̅α , The probability of type II error β
and the power of the hypothesis test P.
Solution: [Write the rules/formula]
Calculate X̅α :
Calculate ZX̅α with the true mean μ = 53:
The probability of type II error β:
The power of the hypothesis test P:

Table-1: Positive z-table NNNNNNNNNNŇ Š Š Š Šm 2345678901234 8849 8869 7734 7764 9505 9515 9931 9932 9961 9854 Table-3: Negative z-table 00010 00007 00005 .00003 34090 33724 23576 23270 20611 20327 17879 17619 15625 15300 00002 00240 .00233 00175 00169 00120 NOT 00064 00062 00045 00043 .00032 .00031 .00030 .00022 .00022 00021 00015 .00015 .00014 00007 00003 .00003 00006 00003 0.05 32636 32270 19766 19489 17106 16853 14457 14917 .14686 00006 00004 00003 131901 18943 .16354 .14007 .00025 .00017 00005 00003 .00002 00003 00002
Transcribed Image Text:Table-1: Positive z-table NNNNNNNNNNŇ Š Š Š Šm 2345678901234 8849 8869 7734 7764 9505 9515 9931 9932 9961 9854 Table-3: Negative z-table 00010 00007 00005 .00003 34090 33724 23576 23270 20611 20327 17879 17619 15625 15300 00002 00240 .00233 00175 00169 00120 NOT 00064 00062 00045 00043 .00032 .00031 .00030 .00022 .00022 00021 00015 .00015 .00014 00007 00003 .00003 00006 00003 0.05 32636 32270 19766 19489 17106 16853 14457 14917 .14686 00006 00004 00003 131901 18943 .16354 .14007 .00025 .00017 00005 00003 .00002 00003 00002
Table-5: t-Table One Tale DF 00 2 3 ........ 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 * * * * * * * * * * 1000 A = 0.1 ta - 1.282 3.078 1.886 1.638 1.533 1.476 1-44 1.415 1.397 1.383 1.372 Baye 1.363 1.303 1.356 1.35 1.345 Tom 1.341 comm 1.337 1.333 1.33 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.31 1.296 1.289 1.282 0.05 1.645 6.314 2.92 2.353 2.132 2.015 1.943 1.895 1.86 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1016 1.746 1.74 1.734 1.729 1.725 P 1.721 1.717 B 1714 1.711 com 1.708 1.706 1.703 1.701 1.699 1.697 1.671 1.658 1.646 0.025 1.96 12.706 4.303 3.182 2.776 B 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2:201 2.179 2.16 2.145 2.131 0.10 2.12 2.11 2.101 2.093 2.086 2.08 2.074 2.069 2.064 0.06 2.06 2.056 2.052 2.048 2.045 2.042 2 1.98 1.962 0.01 2.326 31.821 6.965 4-541 3-747 3.365 3.143 2.998 2,896 2.821 2.764 2:709 2.718 2:718 2.681 2.65 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.5 2.492 2.485 2.479 2.473 2.467 2.462 2-457 2.39 2.358 2.33 0.005 2.576 63.656 9.925 5.841 4.604 4.032 3.707 3-499 3-355 3.25 3.169 3.106 3.100 3.055 3.012 2.om 2.977 2.947 2.921 ... 2.898 .. 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.75 2.66 2.617 2.581 0.001 3.091 318.289 22.328 10.214 7.173 5.894 5.208 4-785 4-501 4.297 4.144 40094 4.025 4:025 3.93 3.852 9787 3-787 3.733 3.686 3.646 261 3.61 3-579 3-552 3-527 3-505 3-485 3.467 3-45 3-435 3-421 3.408 3.396 3.385 3.232 3.16 3.098 0.0005 3.291 636.578 31.6 12.924 8.61 6.869 5-959 5-408 5.041 4.781 4-587 4-437 4-437 4-318 4:221 ..... 4-14 4.073 com 4.015 3.965 3.922 3.883 3.85 3.819 3-792 3.768 3.745 .. 3.725 3.707 3.689 3.674 3.66 3.646 3-46 3-373 3-3 Table-5: t-Table Two Tail DF 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 60 120 8 A = 0.2 ta - 1.282 3.078 1.886 1.638 1.533 1.476 1.415 1.397 1.383 1.372 1.363 1.356 1.35 1.345 1.341 1:341 1.337 1.333 100 1.33 1008 1.328 Loor 1.325 1.323 1.321 1.319 1.318 1.316 1.215 1.315 101 1.314 1.313 1.311 1.31 1.296 1.289 1.282 0.1 1.645 6.314 2.92 2.259 2-353 2 192 2.132 2.015 1.943 1.895 1.86 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1:753 1.746 1.74 1724 1.734 1.729 1.725 ... 1.721 1.717 1.714 1.711 1.708 1.706 1709 1.703 1.701 1.699 1.697 1.671 1.658 1.645 0.05 1.96 t 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.16 2.145 B 2.131 ange 2.12 2.11 2:11 2.101 2.093 2.086 2.00 2.08 2.074 2.069 2.064 2.06 2.056 2052 2.052 2018 2.048 2.045 2.042 2 1.98 1.96 0.02 2.326 31.821 6.965 4-541 3-747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.65 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.5 2.492 2.485 2.470 2-479 2.473 2.467 2.462 2-457 2.39 2.358 2.326 0.01 2.576 63.656 9.925 5.841 +601 4.604 4.032 3.707 Ba 3-499 3.355 3.25 3.169 3.106 3.055 3.012 2.977 com 2.947 2.921 2.898 2.878 2.861 08. 2.845 2.831 2.819 2.807 2.797 2.787 200 2.779 Am 2.771 anta 2.763 2.756 2.75 2.66 2.617 2.576 0.002 3.091 318.289 22.328 10.214 7.173 5.894 .... M 5.208 4-785 4-501 4.297 4.144 4.025 3.93 3.852 3-787 syy 3.733 3.686 3.646 3.61 3-579 3-552 3-527 3-505 3.485 3.467 3.45 3.45 2.425 3-435 0401 3-421 3-408 3.396 3.385 3.232 3.16 3.091 0.001 3.291 636.578 31.6 12.924 8.61 6060 6.869 ..com 5.959 5-408 5.041 B 4.781 4-587 4-437 4-318 4.221 4-14 4.073 4.015 3.965 3.922 3.883 a sc 3.85 0 810 3.819 3-792 3.768 3.745 3.725 3-707 2 680 3.689 3.674 2.66 3.66 3.646 3-46 3-373 3.291
Transcribed Image Text:Table-5: t-Table One Tale DF 00 2 3 ........ 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 * * * * * * * * * * 1000 A = 0.1 ta - 1.282 3.078 1.886 1.638 1.533 1.476 1-44 1.415 1.397 1.383 1.372 Baye 1.363 1.303 1.356 1.35 1.345 Tom 1.341 comm 1.337 1.333 1.33 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.31 1.296 1.289 1.282 0.05 1.645 6.314 2.92 2.353 2.132 2.015 1.943 1.895 1.86 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1016 1.746 1.74 1.734 1.729 1.725 P 1.721 1.717 B 1714 1.711 com 1.708 1.706 1.703 1.701 1.699 1.697 1.671 1.658 1.646 0.025 1.96 12.706 4.303 3.182 2.776 B 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2:201 2.179 2.16 2.145 2.131 0.10 2.12 2.11 2.101 2.093 2.086 2.08 2.074 2.069 2.064 0.06 2.06 2.056 2.052 2.048 2.045 2.042 2 1.98 1.962 0.01 2.326 31.821 6.965 4-541 3-747 3.365 3.143 2.998 2,896 2.821 2.764 2:709 2.718 2:718 2.681 2.65 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.5 2.492 2.485 2.479 2.473 2.467 2.462 2-457 2.39 2.358 2.33 0.005 2.576 63.656 9.925 5.841 4.604 4.032 3.707 3-499 3-355 3.25 3.169 3.106 3.100 3.055 3.012 2.om 2.977 2.947 2.921 ... 2.898 .. 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.75 2.66 2.617 2.581 0.001 3.091 318.289 22.328 10.214 7.173 5.894 5.208 4-785 4-501 4.297 4.144 40094 4.025 4:025 3.93 3.852 9787 3-787 3.733 3.686 3.646 261 3.61 3-579 3-552 3-527 3-505 3-485 3.467 3-45 3-435 3-421 3.408 3.396 3.385 3.232 3.16 3.098 0.0005 3.291 636.578 31.6 12.924 8.61 6.869 5-959 5-408 5.041 4.781 4-587 4-437 4-437 4-318 4:221 ..... 4-14 4.073 com 4.015 3.965 3.922 3.883 3.85 3.819 3-792 3.768 3.745 .. 3.725 3.707 3.689 3.674 3.66 3.646 3-46 3-373 3-3 Table-5: t-Table Two Tail DF 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 60 120 8 A = 0.2 ta - 1.282 3.078 1.886 1.638 1.533 1.476 1.415 1.397 1.383 1.372 1.363 1.356 1.35 1.345 1.341 1:341 1.337 1.333 100 1.33 1008 1.328 Loor 1.325 1.323 1.321 1.319 1.318 1.316 1.215 1.315 101 1.314 1.313 1.311 1.31 1.296 1.289 1.282 0.1 1.645 6.314 2.92 2.259 2-353 2 192 2.132 2.015 1.943 1.895 1.86 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1:753 1.746 1.74 1724 1.734 1.729 1.725 ... 1.721 1.717 1.714 1.711 1.708 1.706 1709 1.703 1.701 1.699 1.697 1.671 1.658 1.645 0.05 1.96 t 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.16 2.145 B 2.131 ange 2.12 2.11 2:11 2.101 2.093 2.086 2.00 2.08 2.074 2.069 2.064 2.06 2.056 2052 2.052 2018 2.048 2.045 2.042 2 1.98 1.96 0.02 2.326 31.821 6.965 4-541 3-747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.65 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.5 2.492 2.485 2.470 2-479 2.473 2.467 2.462 2-457 2.39 2.358 2.326 0.01 2.576 63.656 9.925 5.841 +601 4.604 4.032 3.707 Ba 3-499 3.355 3.25 3.169 3.106 3.055 3.012 2.977 com 2.947 2.921 2.898 2.878 2.861 08. 2.845 2.831 2.819 2.807 2.797 2.787 200 2.779 Am 2.771 anta 2.763 2.756 2.75 2.66 2.617 2.576 0.002 3.091 318.289 22.328 10.214 7.173 5.894 .... M 5.208 4-785 4-501 4.297 4.144 4.025 3.93 3.852 3-787 syy 3.733 3.686 3.646 3.61 3-579 3-552 3-527 3-505 3.485 3.467 3.45 3.45 2.425 3-435 0401 3-421 3-408 3.396 3.385 3.232 3.16 3.091 0.001 3.291 636.578 31.6 12.924 8.61 6060 6.869 ..com 5.959 5-408 5.041 B 4.781 4-587 4-437 4-318 4.221 4-14 4.073 4.015 3.965 3.922 3.883 a sc 3.85 0 810 3.819 3-792 3.768 3.745 3.725 3-707 2 680 3.689 3.674 2.66 3.66 3.646 3-46 3-373 3.291
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