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CHMS 5010 Fall 2023 T5 Homework

A spectrophotometric method is used to measure the Pb²⁺ concentrations in water samples. A series of working standard solutions were then prepared by diluting different amount of the standard stock solution into 25 mL volumetric flasks. 

(a) Calculate the concentration (µg/mL) of the standard stock solution that was added to the flasks. [3 pts]

The working standard solutions were analyzed by the instrument and the absorbance signals obtained are given in the following table.

(b) 

Complete a linear regression analysis for this calibration data by reporting the calibration equation, and standard deviations and 95% confidence interval for the slope and the y-intercept. [10 pts]

(c) Calculate and list the residuals (y_i – y_i^hat), and comment on whether they are scattered around zero and if they display any heteroscedasticity. [5 pts]

Paste plot here:

Comment:

(d) An unknown sample was sent to the laboratory. Five replicate analyses were conducted and 1 mL of sample was used each time and diluted to 10mL. The measurements of the absorbance of the sample were 702.5, 691.2, 751.1, 708.3, 704.6. What is the concentration of Pb²⁺ in the sample and its 95% confidence interval? (Hint: Check whether there is any outlier first) [7 pts]

Any outliers ?________

If so, please provide absorbance value in question _________the G critical __________ and G test values ___________

[Pb²⁺] +/- 95% C.I. =

(e) In order to test whether the sample matrix effect is significant, a standard additions calibration curve was made. An aliquot of 5.0 mL of the unknown sample is accurately added to seven different 25 mL volumetric flasks. Known amounts (given below) of a 200 ppm Pb²⁺ standard stock solution are spiked into the volumetric flasks containing the unknown sample and then the flask is filled to the mark. The absorbance values of solutions containing different concentrations of added Pb²⁺ standard are given in the table below. Determine the slope and y-intercept of the calibration curve by added volume using this method. Determine the concentration of Pb²⁺ (ug/mL) in the sample and the uncertainty (Sx_hat value). Comment on the [Pb²⁺] in the sample as calculated by the two calibration methods [8 pts]

CHMS 5010 Fall 2023 T6 Homework

a) The level of sulphur in batches of aircraft fuel is claimed to be symmetrically distributed with a median value of 0.08%. Successive batches are found to have sulphur concentrations of 0.09, 0.08, 0.10, 0.09, 0.10, 0.09, 0.09, 0.10, 0.11, 0.07, and 0.09%. Use the sign test and the signed rank test to check the manufacturer’s claim (note: both tests cannot use data that is identical to the standard value) [8 pts].

Sign Test

pⁿ = _________

C = ________

P = ________

Reject or retain null hypothesis? _________

Signed-Rank Test

Sum of neg ranks = _________

Sum of pos ranks = _______

Test stat = ________

Critical value = _________

Reject or retain null hypothesis? _________

b) The concentrations (mg /mL) of immunoglobulin G in the blood sera of twelve donors are measured by two methods. The first method is considered standard and the laboratory is concerned the second method is biased low. Use the Wilcoxon signed-rank method to determine whether to reject null hypothesis [5 pts]:

Sum of neg ranks =_________

Sum of pos ranks = _______

Test stat = ________

Critical value = ______

Reject or retain null hypothesis? _________

c) A university chemical laboratory contains nine AAS instruments (A-I). Surveys of the opinions of the research students and academic staff show that the students’ order of preference from most to least preferred for the instruments is I, B, G, A, H, D, C, E, F and that the staff members’ order of preference is I, G, B, D, H, E, C, A, F. Are the opinions of the students and the staff correlated? (please use spearman rank correlation) [8 pts]

Differences in rankings (absolute values)

A:                                                            r = ___________

B:                                                            Critical value:__________

C:                                                            Reject or retain null hypothesis?__________

D:

E:

F:

G:

H:

I:

d) In an inter-laboratory collaborative experiment on the determination of arsenic in coal, samples of coal from three different regions were sent to each of four laboratories. Each laboratory performed a duplicate analysis on each sample, with the results shown below (ug/g)

Verify that there is no significant sample-laboratory interaction (with ANOVA statistics and plots), and test for significant differences between the laboratories to determine if there are any significant differences derived from the laboratories. [13 pts]

Mean square due to interaction effects: ________

F value for interaction effects: __________

F critical value for interaction effects: _________

Are there significant interaction effects?___________

Plots shown here:

Least Sig Difference

Mean square due to measurement error:_________

t-stat: _______

n = __________

C.I. half-width: ___________

Differences b/w labs:

1 vs. 2  ________

1 vs. 3 ________

1 vs  4  _______

2 vs. 3 _________

2 vs. 4 ________

3 vs. 4 ________

Any significant differences?_____________