Statistics Homework Solutions 55

Statistics Homework Solutions 55 - 55 SECTION 3.2 13. (a)...

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Unformatted text preview: 55 SECTION 3.2 13. (a) The uncertainty in the average of 9 measurements is approximately equal to s 9 0 081 3 0 027 cm. ¨ ¡ £ ¨ ¡ ¤£ (b) The uncertainty in a single measurement is approximately equal to s, which is 0.081 cm. 15. (a) Let X 87 0 denote the average of the eight measurements, let s 2 0 denote the sample standard deviation, and let σ denote the unknown population standard deviation. The volume is estimated with X . The uncertainty is σX σ 8 s 8 2 0 8 0 7 mL. ¨ ¡ ¨ ¡ ¨ ¡ 0 5 mL ¡ 16 ¨ ¤£ ¤£ ¤£ 20 ¤£ ¨ ¡ ¡ 16 ¡ ¤£ s ¨ (b) σX (c) Let n be the required number of measurements. Then σ n 0 4. Approximating σ with s 2 0 yields 2 0 n 0 4, so n 25. ¨ ¡ ¤£ ¨ ¤£ ¨ ¨ ¡ Let X denote the average of the 10 yields at 65 C, and let Y denote the average of the 10 yields at 80 C. Let sX denote the sample standard deviation of the 10 yields at 65 C, and let sY denote the sample standard deviation of the 10 yields at 80 C. Then X 70 14, sX 0 897156, Y 90 50, sY 0 794425. 17. ¨ ¡ ¤£ ¡ 20 36. 282 0 38. ¨ ¨ ¡ 5 0 016. 0 0089. ¨ ¨ ¤£ ¡ ¨ ¡ ¤£ ¤£ ¨ ¢ ¨ ¡ ¤ ¡ ¡ ¤£ ¢ ¡ ¡ 2 ¤¥ 13 0 022 5 ¨ £¤ ¢¥ ¤ ¨ ¢¥ 0 052 10 £ ¨ £ ¨ 2 £ ¤¥ £ £¤ ¨ ¤ ¡ ¨ ¡ ¥ ¢ ¨ £¤ ¢ is smaller. 23 ¡¥ ¡ ¡ ¨ 2 1 3 2σY 0 0091. 0 011. ¨ ¨ is 0 52 0 022 5 ¡¥ ¢ 5 15 Y 0 52 0 052 10 ¨ 2 0 52σY ¢ ¨ ¥ 1 2Y 0 02 10 is 2 3 2 σ2 X ¡ ¢ £¤ ¡ ¢ ¡ ¡ ¢ ¦ ¢ ¡ ¢ ¦ 1 The uncertainty in 2 X 5 0 05 ¤£ ¨ ¡ ¡ 10 15 X σY 10 ¡ ¨ ¨ ¤£ 0 5 2 σ2 X σX ¨ ¡ ¨ ¡ 1 3Y 1 2Y ¨ ¨ 0 0 25. ¨ ¤£ 0 5Y 3X 0 70 14 252 90 50 0 02 denote the uncertainty in the instrument. Then σY The uncertainty in σ2 90 50 10 0 28. 0 05 denote the uncertainty in the instrument. Then σX (c) The uncertainty in 1 X 2 σ0 5X X σ2 X 70 14 ¡ (b) Let σY 0 794425 ¨ 19. (a) Let σX 90 50 10 ¡ X 0 897156 ¨ ¨ The uncertainty is σY 2 σY ¡ (b) The difference is estimated with Y ¨ 10 ¡ sY 70 14 ¨ At 80 C, the yield is Y 10 ¡ sX ¨ (a) At 65 C, the yield is X ...
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This note was uploaded on 12/20/2011 for the course STA 3163 taught by Professor Mattgilg during the Fall '11 term at UNF.

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