The following results were obtained for the determination of calcium in a NIST limestone sample: % CaO = 50.32, 50.22, 50.40, 50.21, and 50.44. Five gross samples were then obtained for a carload of limestone. The average percent CaO values for the gross samples were found to be 49.47, 50.10, 49.58, 49.76, and 50.49. Calculate the relative standard deviation associated with the sampling step. Relative standard deviation =

The following results were obtained for the determination of calcium in a NIST limestone sample: % CaO = 50.32, 50.22, 50.40, 50.21, and 50.44. Five gross samples were then obtained for a carload of limestone. The average percent CaO values for the gross samples were found to be 49.47, 50.10, 49.58, 49.76, and 50.49. Calculate the relative standard deviation associated with the sampling step. Relative standard deviation =

Fundamentals Of Analytical Chemistry

9th Edition

ISBN:9781285640686

Author:Skoog

Publisher:Skoog

Chapter8: Sampling, Standardization, And Calibration

Section: Chapter Questions

Problem 8.5QAP

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The following results were obtained for the determination of calcium in a NIST limestone sample: %CaO = 50.33, 50.22, 50.36, 50.21, and 50.44. Five gross samples were then obtained for a carload of limestone. The average %CaO values for the gross samples were found to be 49.53, 50.12, 49.60, 49.87, and 50.49. Calculate the relative standard deviation associated with the sampling step
Analysis of several plant-food preparations for potassium ion yielded the following data: Sample Percent K+ 1 3.90, 3.96, 4.16, 3.96 2 4.48, 4.65, 4.68, 4.42 Find the mean ; standard deviation variance and RSD for each sample.
Calculate the standard deviation for an element whose % in a sample were found to be20.8, 21.6, 22.1, 22.0, 23.3, 21.9 and 22.8%
Titration of an oxalate sample gave the following percentages: 15.07 % , 15.58 % , and 15.42 % . Calculate the average. Calculate the standard deviation.
A titrimetric method for the determination of calcium in limestone was tested with the analysis of a NIST limestone containing 30.15% CaO. The mean of the four analyzes is 30.26% CaO with a standard deviation of 0.085%. From the data accumulated from many analyzes, s→ϭ=0.094% CaO was found.a) Do the data indicate the presence of systematic error at the 95% confidence level?b) When a value for ϭ is unknown, do the data show a systematic error at the 95% confidence level?
An atomic absorption method for the determination of the amount of iron present in used jet engine oil was found from pooling 30 triplicate analyses to have a standard deviation s = 3.6 mg Fe/mL. If s is a good estimate of σ, calculate the 95 and 99% confidence intervals for the result 18.5 mg Fe/mL if it was based on (a) a single analysis, (b) the mean of two analyses, and (c) the mean of four analyses.
A titrimetric method for the determination of calcium in limestone was tested by analysis of an NIST limestone containing 30.15% CaO. The mean result of four analyses was 30.26% CaO, with a standard deviation of 0.085%. By pooling data from several analyses, it was established that s   = 0.094% CaO.a. Do the data indicate the presence of a systematic error at the 95% confidence level?b. Do the data indicate the presence of systematic error at the 95% confidence level if no pooled value for s was available?
A young researcher was evaluating a standard method for determining the methylmercury content in blue fin tuna using high performance liquid chromatography (HPLC). She determined the standard deviation (?)(s) for the method to be 0.440.44 ppb and assumed that ?s was a good approximation of ?σ . As a test, she used this method to evaluate the methylmercury content in a National Institutes of Standards and Technology (NIST) standard and determined the unknown amount to be within 0.210.21 ppb (?)(μ) of the known mean with 99% probability. How many replicate measurements of the NIST standard did the researcher perform?
3. Seven analyses for the phosphorus content of a fertilizer resulted in 16.2, 17.5, 15.4, 15.9, 16.8, 16.3, and 17.1%. Find (a) the standard deviation, s, , and (b) the 95% confidence interval for the true value, H. 4. The following five values were obtained for the wt % of an organic acid in a sample: 30.3, 31.1, 32.6, 36.7, 28.9. Determine if the value of 36.7 may be rejected at the 90% (two-tailed) confidence level. 5. The concentration of a NaOH solution is determined in a single experiment by titrating a weighed sample of pure, dried KHP (MW = 204.229) with the NaOH. The data are: Weight of KHP = (11.6723 + 0.0001) - (10.8364 ±0.0001) g Volume NaOH = (32.68 + 0.02) - (1.24 + 0.02) mL Where the standard deviations are o, values. (a) What is the molarity of the NaOH? (b) Based on the propagation-of-error formula, what is the standard deviation of the molarity,oM ?
An atomic absorption method for the determination of the amount of iron present in used jet engine oil was found from pooling 30 triplicate analyses to have a standard deviation s = 3.1 µg Fe/mL. If s is a good estimate of o, calculate the 95 and 99% confidence intervals for the result 21.7 µg Fe/mL if it was based on the following criteria. (a) a single analysis 95% confidence interval= 21.7 + 99% confidence interval = 21.7 + (b) the mean of two analyses 95% confidence interval = 21.7 + 99% confidence interval= (c) the mean of six analyses 21.7 ± 95% confidence interval = 21.7 + 99% confidence interval= 21.7 + μg Fe/mL μg Fe/mL μg Fe/mL μg Fe/mL μg Fe/mL μg Fe/mL
To test the quality of the work of a commercial laboratory, duplicate analyses of apurified benzoic acid (68.8% C, 4.953% H) sample were requested. It is assumed that therelative standard deviation of the method is sr →  = 4 ppt for carbon and 6 ppt forhydrogen. The means of the reported results are 68.5% C and 4.882% H. At the 95%confidence level, is there any indication of systematic error in either analysis?
Why is Spooled a better estimate of s than the standard deviation from any one sample?