Question

Two catalysts in a batch chemical process, are being compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1, and a sample of 10 batches was prepared using catalyst 2. The 12 batches for which catalyst 1 was used in the reaction gave an average yield of 85 with a sample standard deviation of 4, and the 10 batches for which catalyst 2 was used gave an average yield of 81 and a sample standard deviation of 5. Find a 90% confidence interval for the difference between the population means, assuming that the populations are approximately normally distributed with unequal variances.

Answer 1

Solution

Given Information:

Sample 1:

Sample size (n1): 12

Mean value = 85

Standard deviation = 4

Sample 2:

Sample size (n2) = 10

Mean Value = 81

Standard Deviation = 5

Following formula can be used to calculate the confidence interval:

t score can be determined on the basis of confidence level and degrees of freedom

df = n₁ - 1 or n₂ - 1

df = 12-1 = 11

By referring to the t-distribution table, the t-score at 90% confidence level and df = 11 is 1.796

We are 90% confident that the differrence between population means is between 0.486 and 7.514.