Answer Happy

Imagine that you conduct a small Christmas experiment with a group of friends. You are interested in how far a cork can fly when you pop a bottle of champagne. You cool fifteen bottles of the same brand and vintage of champagne wine to the temperature of 10 degrees and one person opens them all (one by one) using the same technique and you measure the distance the corks have flown. The measured distances in meters are given in Table 2. 1.1 1.5 1.3 2.9 2.6 3.5 1.9 2.6 2.6 4.1 3.4 2.6 3.2 3.3 3.4 Table 2: Observations for Problem 26, distance the corks have flown in meters Suppose that the distances the corks fly are independently and normally distributed. i) What is the 90% confidence interval of the mean distance? ii) Beside the mean distance you are interested in the distance deviation. What is the 90% confidence interval of the variance? iii) How does the answer to part ii) change if you assume to know that the true mean distance is 3 meters.