Question

A) 28 units of sample were taken from a main mass and the average of this sample was calculated as 12 and the standard deviation as 5. Calculate the confidence limits of the mean mass at the 5 percent error level.

Answer 1

Solution :

A) The error level is 5 percent. It means we need to find the confidence limits for the population mean at (100% - 5%) = 95% confidence level.

The confidence limits of the population mean at 95% confidence level is given as follows :

Where, x̅ is sample mean, s is sample standard deviation, n is sample size and t_{(0.05/2, n - 1)} is critical t-value at 95% confidence level and (n - 1) degrees of freedom.

We have,  x̅ = 12, s = 5 and n = 28

Using t-table we get, t_{(0.05/2, 28 - 1)} = 2.052

Hence, confidence limits of mean at 95% confidence level is,

Lower confidence limit = 10.06

Upper confidence limit = 13.94

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