Question

Exercise 12

The U.S. Dairy industry wants to estimate the mean yearly milk consumption. A sample of 16 people reveals the mean yearly consumption to be 60 gallons with a standard deviation of 20 gallons. Assume the population distribution is normal.

• Explain which words in the problem indicate a z-distribution or a t-distribution (choose one).
• Show how to calculate the confidence interval using Excel or typing out the equation (such as for proportions). The purpose is to identify a correct equation (with numbers typed out for all to learn) to solve these problems

Answer 1

As we are given here that the population distribution is normal, therefore we can use the Z distribution here to obtain the confidence interval.

Let us compute a 95% confidence interval here.

From standard normal tables, we have:
P(-1.96 < Z < 1.96) = 0.95

Therefore the 95% confidence interval for population mean here is obtained as:

This is the required 95% confidence interval for population mean here.