Question

The Packaging Company produces boxes out of cardboard and has a specified weight of 8 oz. A random sample of 20 boxes cans yielded a sample mean of 7.5 oz. Given the data's distribution is normally distributed and standard deviation is 1.4 oz, for a 95% confidence interval, what is the lower confidence limit? What is the standard error? What is the estimated margin of error?

Answer 1

Here in this scenario it is given that the  Packaging Company produces boxes out of cardboard and has a specified weight of 8 oz. A random sample of 20 boxes cans yielded a sample mean of 7.5 oz.

Assuming that the data is normally distributed with population Standerd deviation 1.4 oz.

Now we need to use z distribution for computing the Confidence Interval for population mean.

Using z critical value we computed the 95% Confidence Interval for population mean is given formula below,

The z critical value is calculated using Standerd normal z-table.

The lower Confidence limit is 6.886.

The Standerd error is 1.4/√20 = 0.3130.

The margin of error is 1.96*0.3130 = 0.614.

Hope it helps.

Thank you.