Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle is determined.  Let  denote the average alcohol content for the population of all bottles of the brand under study.  Suppose that the sample of 50 results in a 95% confidence interval for  of (7.8, 9.4).  a) Would a 90% confidence interval have been narrower or wider than the given interval?   b) If the sample size was increased to 100, would the confidence interval be narrower or wider than the given interval?   c) Explain what we mean by the “We are 95% confident” part of the interpretation.

Use the t-distribution to find a confidence interval for a difference in means y, - M, given the relevant sample results. Give the best estimate for 41 - M2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed. A 99% confidence interval for My - A using the sample results x1 = 546, S, = 117, m, = 340 and X2 = 451,52 = 90, M2 = 200 Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places. Best estimate = Margin of error = Confidence interval

A district official intends to use the mean of a random sample of 150 sixth graders from a very large school district to estimate the mean score that all the sixth graders in the district would get if they took a certain arithmetic achievement test. If, based on experience, the official knows that = 9.4 for such data, suppose that the district official takes her sample and gets = 61.8. Use all the given information to construct a 99% confidence interval for the mean score of all the sixth graders in the district.

A researcher constructs a confidence interval using the value z*=1.44. What confidence level does their interval have