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Filet Mignon and Weight Hypothesis Testing

I love filet mignon. The full cut is supposed to weigh 16 ounces when fully cooked. My restaurant serves 200 servings of filet mignon per day. The restaurant claim is they serve filets that are 16 ounces with a standard deviation of .4 ounces due to shrinking while cooking. I ate filet mignon for 16 days straight. The average weight of all the servings was 15.4 ounces. Using a = .10, can I make a public statement and back it up with hypothesis testing that the average filet is actually less that 16 ounces?

Solution Summary

This solution provides a null and alternative hypothesis and computes the z-statistics and compares it to the p-value to make a decision on whether or not to accept or reject the null hypothesis. All steps are shown with explanations.