Answer Happy

The group of friends from Problem 26 is not satisfied with the results of their experiment. Many of them lost a bet hoping that the average distance will be at least three meters. On the New Year's Eve they repeat the experiment with another brand of champagne. The conditions of the experiment remain the same same temperature of the bottles, same room temperature etc.) and the same person opens another fifteen bottles of champagne of this other brand. The new measured distances in meters are given in Table 4. 4.2 2.6 3.3 3.5 2.3 3.2 3.8 3.0 2.1 2.5 2.2 2.8 1.9 2.4 3.0 Table 4: Observations for Problem 29, distance the corks of the second brand of champagne have flown in meters i) Construct a 99% confidence interval for the mean distance the corks of the second brand of champagne fly. Using the confidence interval, test whether this time the mean distance is equal to 3.2 meters. ii) Test if the brand of champagne does influence the final distance the corks are flying at 1% significance level. (Contrary to Problem 26 iii), consider that you do not know the true value of the mean distance.) What additional assumptions do you need in order to perform this test? If possible, test these assumptions as well.