Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected, and the alcohol content of each bottle is determined. Let mu denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.8, 9.4).
Would a 90% confidence interval calculated from the sample sample have been narrower or wider than the given interval? Explain your reasoning.
Consider the following statement: There is a 95% chance that the population mean is between 7.8 and 9.4. Is this statement correct? Why or why not?
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In this solution, the effect of changing confidence levels on the width of a confidence interval is explainedl. It is also explained how to interpret the results when we create a confidence interval.