# Testing a Hypothesis and Confidence Interval

1. The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.

A. What is the value of the population mean? What is the best estimate of this value?

B. Explain why we need to use the t distribution. What assumption do you need to make?

C. For a 90 percent confidence interval, what is the value of t?

D. Develop the 90 percent confidence interval for the population mean.

E. Would it be reasonable to conclude that the population mean is 63 pounds?

2. A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 4 pounds, the standard deviation 0.5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than 0.2 pounds?

3. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

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#### Solution Summary

This solution contains detailed explanations of testing hypotheses of population means and computing confidence interval of the population mean.