Question

The average weight of 25 samples randomly selected from the products produced in a factory is 1100 g.
The standard deviation of the sample was measured as 20 g. Accordingly, in what range is the average weight of the sample produced with a confidence level of 92%?

Answer 1

Solution :

The 92% confidence interval for population mean is given as follows :

Where, x̅ is sample mean, s is sample standard deviation, n is sample size and t(0.08/2, n - 1) is critical t-value to construct 92% confidence interval.

We have,  x̅ = 1100 g, s = 20 g, n = 25

Using t-table we get, t(0.08/2, 25 - 1) = 1.828

Hence, 90% confidence interval for average of the products produced in the factory is,

Hence, the range of the average weight of the sample produced with a confidence level of 92% is (1092.688, 1107.312).