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The rare earth element gadolinium is often used as a contrasting agent for MRIs. The concentration of gadolinium was measured in the discharge from a wastewater treatment plant near a large medical facility. Eight measurements were obtained: 1.353 ppm, 1.358 ppm, 1.341 ppm, 1.346 ppm, 1.916 ppm, 1.349 ppm, 1.356 ppm, 1.349 ppm. Use the Grubbs test to determine if one of these values is an outlier. What is the value of Gcalc ?

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Answer:

One of the values is an outlier (1.916)

Gcalc = 2.475

Explanation:

Using the Grubbs test:

Sorted values :

1.341

1.346

1.349

1.349

1.353

1.356

1.358

1.916

Mean of data (m) : ΣX / n

n = number of observations

(1.341 + 1.346 + 1.349 + 1.349 + 1.353 + 1.356 + 1.358 + 1.916) / 8

= 11.369 / 8

= 1.421

Standard deviation(sd) : Σ(X - m) / n

To save computation time, we can obtain standard deviation using a calculator :

Standard deviation = 0.200

Scrubb test statistic (G) :

max|X - m| / sd

| 1.341 - 1.421 | / 0.200 = 0.400

| 1.346 - 1.421 | / 0.200 = 0.375

| 1.349 - 1.421 | / 0.200 = 0.36

| 1.349 - 1.421 | / 0.200 = 0.36

| 1.353 -1.421 | / 0.200 = 0.34

| 1.356 - 1.421 | / 0.200 = 0.325

| 1.358 - 1.421 | / 0.200 = 0.315

| 1.916 - 1.421 | / 0.200 = 2.475

((Xmax - X) / sd) = 2.475

Z score = 2.475

The P-value as obtained from the p value calculator for a Zscore of 2.475 is 0.013324.

The result is significant at p< 0.05

Hence, the outlier is 1.916

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