An APC tablet (Aspirin, Phenacetin, Caffeine) is known to contain 0.5500 % caffe

Question

An APC tablet (Aspirin, Phenacetin, Caffeine) is known to contain 0.5500 % caffeine. A new method of caffeine analysis was used to measure the caffeine content 6 times. A) Using all six analyses in the table below, is this new method significantly different at the 90% CL? B) Show by a G test if one of the outlying data points can or cannot be excluded at the 90%CL C) If so, is the new method significantly different at the 90% CL with the data point excluded? 9. NEATLY SHOW ALL WORK/SETUPS!) Grubb's Test for % caffeine 0.6487 0.5580 0.5552 0.5546 0.5529 0.5503 Number of Observations 90% 1.148 1.452 1.602 1.729 1.929 1.909 1.977 102.036 2.088 12 2.134 13 2.175 2.213 15 2.247 16 2.279 2.309 18 2.335 2361 2.385 14 17 19

Explanation / Answer

Solution:

(A)

The mean or average of the given measurements can be calculated using the below formula.

x = (x1 + x2 + x3 + x4 + x5 + x6) / 6

Here, x1 = 0.6487, x2 = 0.5580, x3 = 0.5552, x4 = 0.5546, x5 = 0.5529 and x6 = 0.5503

By substituting all the above values, you will get x = 0.56995

The standard deviation of the measurements can be calculated as shown below.

s = [{(x1 - x)2 + (x2 - x)2 + (x3 - x)2 + (x4 - x)2 + (x5 - x)2 + (x6 - x)2}/(6-1)]1/2

By substituting all the above values, you will get s = 0.03866

The 90% confidence level can be calculated as shown below.

(x ± ts/n1/2), where t = 90% confidence limit = 1.645, n = no. of measurements = 6

ts/n1/2 = 1.645*0.03866/61/2 = 0.02596

Now, the 90%confidence interval = (0.56995 - 0.02596, 0.56995 + 0.2596) = (0.54399, 0.59591)

Yes, the new method is significantly different at the 90% C.L.

(B)

By applying Grubb's test,

G = max{mod(xi-x)}/s

i.e. G = (0.6487 - 0.56995) / 0.03866 = 2.037

The given Grubb's test for outliers = 1.729

Therefore, the calculated value is greater than the given value, hence one of the outlying data points can be excluded.

(C)

Yes, the new method is significantly different at the 90% C.L. with the data point excluded.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.