Question

(a) During the verification of a method, you have repeated analysis of an analyte X in a certified reference material (CRM), with the results as follows: 210 mg/kg, 217 mg/kg, 220 mg/kg, 221 mg/kg, 208 mg/kg, 211 mg/kg (i) Determine the mean and standard deviation of your results. [4 marks] (ii) The reference value of X in CRM was shown to be 208.8 ± 6.74 mg/kg. Under 95% confidence level, conduct a student t-test to determine whether the results obtained are significantly different from the reference value. [4 marks] (b) Table below summarized the total mould and yeast testing results (cfu = colony-forming unit) from the production samples of a yogurt factory. The results were collected on different days, in duplicate, by different analysts, using different equipment (e.g. balances, pipettors) and possibly using different batches of media/reagents. Date | 1st trial (cfu/g) | 2nd trial (cfu/g) 7 July 2020 | 1.20 × 10^5 | 1.58 × 10^5 21 July 2020 | 2.62 × 10^5 | 1.78 × 10^5 4 August 2020 | 2.15 × 10^5 | 2.76 × 10^5 18 August 2020 | 1.85 × 10^5 | 2.65 × 10^5 1 September 2020 | 1.38 × 10^5 | 1.03 × 10^5 15 September 2020 | 1.21 × 10^5 | 1.62 × 10^5 Assuming there is no other component contributed to the measurement uncertainty, by using log 10 transformation, determine the relative standard deviations of reproducibility (RSDR) and the expanded uncertainty (where k = 1.96). [9 marks] (c) The resulting colony count of today’s sample was found to be 1.30 × 10^5 cfu/ml. Determine the confidence interval of resulting colony count in this yogurt sample. [6 marks] (d) In case the routine colony counts for microbiological testing were found less than 10 cfu, what precaution measure will be taken for estimation of measurement uncertainty due to precision? [2 marks]

          (a) During the verification of a method, you have repeated analysis of an analyte X in a certified reference material (CRM), with the results as follows:
210 mg/kg, 217 mg/kg, 220 mg/kg, 221 mg/kg, 208 mg/kg, 211 mg/kg
(i) Determine the mean and standard deviation of your results. [4 marks]
(ii) The reference value of X in CRM was shown to be 208.8 ± 6.74 mg/kg. Under 95% confidence level, conduct a student t-test to determine whether the results obtained are significantly different from the reference value. [4 marks]
(b) Table below summarized the total mould and yeast testing results (cfu = colony-forming unit) from the production samples of a yogurt factory. The results were collected on different days, in duplicate, by different analysts, using different equipment (e.g. balances, pipettors) and possibly using different batches of media/reagents.
Date | 1st trial (cfu/g) | 2nd trial (cfu/g)
7 July 2020 | 1.20 × 10^5 | 1.58 × 10^5
21 July 2020 | 2.62 × 10^5 | 1.78 × 10^5
4 August 2020 | 2.15 × 10^5 | 2.76 × 10^5
18 August 2020 | 1.85 × 10^5 | 2.65 × 10^5
1 September 2020 | 1.38 × 10^5 | 1.03 × 10^5
15 September 2020 | 1.21 × 10^5 | 1.62 × 10^5
Assuming there is no other component contributed to the measurement uncertainty, by using log 10 transformation, determine the relative standard deviations of reproducibility (RSDR) and the expanded uncertainty (where k = 1.96). [9 marks]
(c) The resulting colony count of today’s sample was found to be 1.30 × 10^5 cfu/ml. Determine the confidence interval of resulting colony count in this yogurt sample. [6 marks]
(d) In case the routine colony counts for microbiological testing were found less than 10 cfu, what precaution measure will be taken for estimation of measurement uncertainty due to precision? [2 marks]

(a) During the verification of a method, you have repeated analysis of an analyte X in a certified reference material (CRM), with the results as follows:
210 mg/kg, 217 mg/kg, 220 mg/kg, 221 mg/kg, 208 mg/kg, 211 mg/kg
(i) Determine the mean and standard deviation of your results. [4 marks]
(ii) The reference value of X in CRM was shown to be 208.8 ± 6.74 mg/kg. Under 95% confidence level, conduct a student t-test to determine whether the results obtained are significantly different from the reference value. [4 marks]
(b) Table below summarized the total mould and yeast testing results (cfu = colony-forming unit) from the production samples of a yogurt factory. The results were collected on different days, in duplicate, by different analysts, using different equipment (e.g. balances, pipettors) and possibly using different batches of media/reagents.
Date | 1st trial (cfu/g) | 2nd trial (cfu/g)
7 July 2020 | 1.20 × 10^5 | 1.58 × 10^5
21 July 2020 | 2.62 × 10^5 | 1.78 × 10^5
4 August 2020 | 2.15 × 10^5 | 2.76 × 10^5
18 August 2020 | 1.85 × 10^5 | 2.65 × 10^5
1 September 2020 | 1.38 × 10^5 | 1.03 × 10^5
15 September 2020 | 1.21 × 10^5 | 1.62 × 10^5
Assuming there is no other component contributed to the measurement uncertainty, by using log 10 transformation, determine the relative standard deviations of reproducibility (RSDR) and the expanded uncertainty (where k = 1.96). [9 marks]
(c) The resulting colony count of today’s sample was found to be 1.30 × 10^5 cfu/ml. Determine the confidence interval of resulting colony count in this yogurt sample. [6 marks]
(d) In case the routine colony counts for microbiological testing were found less than 10 cfu, what precaution measure will be taken for estimation of measurement uncertainty due to precision? [2 marks]

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