Question

Students measured the concentration of HCI in a solution by titrating with different indicators to find the end point. (Use the table to find critical F values.) Mean HCl concentration (M) (t standard deviation) Indicator Number of measurements 1. Bromothymol blue 0.09565 0.00232 28 2. Methyl red 0.08688 t 0.00098 18 3. Bromocresol green 0.08641 t 0.001 15 29 Is the difference between indicators 1 and 2 significant at the 95% confidence level? Yes No Fcalculated degrees of freed om tcalculated Is the difference between indicators 2 and 3 significant at the 95% confidence level? Yes No Fcalculated Spooled tcalculated

Answer 1

Pg 1 Tormulae Used Sildf, 1 dfan, F-statistic ~ ~ Fedf, effe) e af ml Ferra S²/de t-statistic – u tom, the 2 tv, 4 , -2 where ² Ins? + M₂ S₂² nit 1₂ - 2 (1,-1) 5D, 2 + (^2-1) SD ² Spooled = 1 Mgan₂-2 Given n = 28 n =18 = 29 a = 0.09565 0.08688 x = 0.08641 s² = (0.00232)² = 0.538245105 s (0.00098)" = 0.09604 x 10-1 s? Co. 00115 0.13 228 x 100

(P2) Is the difference between indicatos 1 and 2 significant at 98% confidence inlened! 5² 28 (0.53824 910) + 18x10.09804 x 10')] x [1/44] 1.1 [0.000151 & 0.00001737 144 = 0.3825 + 105 Statistic Degrees of fuedan 1 Calculated value 27, 17 0.53824770"/27 - 3.53 0.09804 4107/17 1917 0.09565-0.08680 44 1 0.38 257 10 *(18) 14.296 Now, but at 95% is 2.17 and calculated F (22, 12) = 3.53 a And tabulated tun at 95% is (-2.015, 2018) and Kalculated tan = 14.246 / Therefore, there is significant difference in indicator I and 2.

2 indicator 2 and 3 sign to the difference between at 99% ca. > ,- s?[18(0-9604430-) + 29% (0.13225.1104)«[1/5] [0.000173 & c. odoo 384] (45 2 0.47 P10 Calculated value Statistic D.-/ 17,28 1.1961 0.00047 = Or 2168 - 2-168 /0-3 The calculated Fig, 20 = 1.961 and tobulated F12, 28 at 95% CI 1.99. The calculated tur 207 0.2168 and tobulolid tur at 95% ca 2 2.014 Therefore there is no significant difference indicator 2 and 3. between

Howeet 17*(0.09604x10-5) + 28 x (0.13225810) Spooled = 18+ 29-2 ملاصدع و 0.1633410-4 + 37.03 x 10-4 45 10.8265 xlorf = 0.000 909

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