Question

A 15 unit sample of the chemical potency of a solvent is drawn and provides the following results: The mean is 23 µg / ml and a standard deviation of 1.2 µg / ml. Calculate the confidence interval for the average potency of the solvent with 90% confidence.

Answer 1

Sample size = n = 15

Sample mean = = 23

Sample standard deviation = s = 1.2

Confidence level = c = 0.90

alpha = 1 - c = 1 - 0.90 = 0.1

Here population standard deviation is not known so we use t test.

90% Confidence interval for the average potency of the solvent is

where tc is t critical value for alpha = 0.1 and degrees of freedom = n - 1 = 15 - 1 = 14

t critical value from excel using function:

=T.INV.2T(0.1,14)

tc = 1.761 (Round to 3 decimal)

(Round to 2 decimal)

90% Confidence interval for the average potency of the solvent is (22.45, 23.55)