For full credit, you must show All your work and Explain All your answers! Point values given are those I will use If I choose to grade that problem

1. In Project 1 this Fall you studied Recording Times in minutes for Dr. Marion's Sample of 28 Recordings of Mahler's 9th Symphony, which are:

80 82 78 80 89 87 79 90 84 88 81 81 81 86 85 77 84 77 82 85 81 91 82 86 86 89 70 81

a. Estimate the Mean Length of all Recordings All Mahler's 9th Symphony.

b. To draw any inferences from these data, what must we assume and why?

c. For the Mean Recording Time of all Recordings of Mahler's 9th Symphony

i. Find a 95% Confidence Interval.

ii. Find a 99.5% Confidence Interval.

iii. Which of your two intervals is wider, and why?

d. What Hypotheses would you use to test at = 0.025 that the Mean Recording Time for Mahler's 9th Symphony is significantly less than 85 minutes? Define in words any parameters you use in your Hypotheses.