- The mean for these statistic is equal to 0.1675.
- The standard deviation for these statistic is equal to 0.0149.
- The confidence interval at 95% is 0.1675 ± 0.0104.
- The method detection limit (MDL) is equal to 0.035 mg/L.
- The estimated practical quantitation limit (PQL) is equal to 29.8 mg/L.
- Yes, it is accurate to measure samples containing Cr⁶⁺ around 0.1 mg/L because it's greater than 0.0875 mg/L.
How to calculate the mean of a statistic?
Mathematically, the mean for these statistic can be calculated by using the following formula:
Mean = [F(x)]/n
For the total number of data, we have:
F(x) = 0.195 + 0.167 + 0.178 + 0.151 + 0.176 + 0.155 + 0.154 + 0.164
F(x) = 1.34.
Substituting the parameters into the formula, we have:
Mean = [F(x)]/n
Mean = [1.34]/8
Mean = 0.1675.
How to calculate the standard deviation?
Mathematically, the standard deviation for these statistic can be calculated by using the following formula:
σ = √(x - μ)²/(n - 1)
(x - μ)² = [(0.195 - 0.1675)² + (0.167 - 0.1675)² + (0.178 - 0.1675)² + (0.151 - 0.1675)² + (0.176 - 0.1675)² + (0.155 - 0.1675)² + (0.154 - 0.1675)² + (0.164 - 0.1675)²]
(x - μ)² = [0.0275² + 0.0005² + 0.0105² + 0.00165² + 0.0085² + 0.0125² + 0.0135² + 0.0035²].
(x - μ)² = [0.0007563 + 0.00000025 + 0.0001103 + 0.0002723 + 0.00007225 + 0.0001563 + 0.0001823 + 0.0001225].
(x - μ)² = 0.001562.
Substituting the parameters into the formula, we have:
σ = √0.001562/(8 - 1)
σ = √0.001562/7
σ = √0.00022314285714286
Standard deviation, σ = 0.0149.
How to calculate the confidence interval?
First of all, we would calculate the standard error of the mean (SEM) as follows:
SEM = σ/√n
SEM = 0.0149/√8
SEM = 0.0053.
Alpha, α = 1 - 95/100
Alpha, α = 1 - 0.95
Alpha, α = 0.05
Critical probability (p*) = 1 - α/2
Critical probability (p*) = 1 - 0.05/2
Critical probability (p*) = 0.975.
From the z-table, the z-score is given by:
Zα/2 = 1.960.
Margin of error is given by:
Margin of error, E = 1.960 × 0.0053
Margin of error, E = 0.0104.
Therefore, the confidence interval at 95% is given by:
p - E < p < p + E
0.1675 - 0.0104 < p < 0.1675 + 0.0104
Confidence interval = 0.1675 ± 0.0104.
How to calculate the method detection limit (MDL)?
MDL = Student’s t value × Standard deviation.
MDL = 2.365 × 0.0149
MDL = 0.035 mg/L.
How to calculate the estimated practical quantitation limit (PQL)?
PQL = 100/α × Standard deviation.
PQL = 100/0.05 × 0.0149
PQL = 29.8 mg/L.
How to determine the accuracy?
In order to determine the accuracy, we would calculate the lower limit from the method detection limit (MDL) as follows:
Lower limit = 2.5 × MDL
Lower limit = 2.5 × 0.035
Lower limit = 0.0875 mg/L.
In conclusion, we can infer and logically deduce that it is accurate to measure samples containing Cr⁶⁺ around 0.1 mg/L because it's greater than the "lower limit" of 0.0875 mg/L.
Read more on confidence interval here: brainly.com/question/24156808
#SPJ1
