Find the 50% and 90% confidence interval for the carbohydrate content.?

Question

In replicate analyses, the carbohydrate content of a glycoprotein (a protein with a sugar attached to it) is found to be 12.6, 11.9, 13.0, 12.7, and 12.5 grams of carbohydrate per 100g of protein. Find the 50% and the 90% confidence interval for the carbohydrate content.

Answer 1

ANSWER:  90% CONFIDENCE INTERVAL = [12.2, 12.9]

ANSWER:  50% CONFIDENCE INTERVAL = [12.4, 12.7]

Why???

SMALL SAMPLE, CONFIDENCE INTERVAL, NORMAL POPULATION DISTRIBUTION

x-bar = Sample mean [12.54]

s = Sample standard deviation [0.404]

n = Number of samples [5]

df = degrees of freedom [5 - 1 = 4]

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For confidence level of 90%, two-sided interval ("look-up" from Table) "t critical value" [2.13]

Resulting Confidence Interval for "true mean":

x-bar +/- (t critical value) * s/SQRT(n) = 12.54 +/- 2.13 * 0.404/SQRT(5) = [12.2, 12.9]

ANSWER: 90% Confidence Interval [12.2, 12.9]

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For confidence level of 50%, two-sided interval ("look-up" from Table) "t critical value" [0.741]

Resulting Confidence Interval for "true mean":

x-bar +/- (t critical value) * s/SQRT(n) = 12.54 +/- 0.741 * 0.404/SQRT(5) = [12.4, 12.7]

ANSWER: 50% Confidence Interval  [12.4, 12.7]