Question

In Project 1 this Spring, you studied recording times in minutes for a sample of Dr. Marion’s 33 recordings of Gustav Mahler’s 1st Symphony: 55 49 50 52 53 56 55 53 57 59 52 55 50 50 62 53 58 58 63 51 52 51 54 65 60 57 57 56 54 56 47 48 52

Using σ = 4, how large a sample would we need in order to estimate mean recording times for Mahler’s 1st Symphony to a:

i. 95% error margin of 3 minutes?

ii. 90% error margin of 2 minutes?

iii. Compare your answers and explain their difference.

Answer 1

σ = 4

i. 95% error margin of 3 minutes?

E = 3

z_c = 1.96

n = 7

ii. 90% error margin of 2 minutes?

E = 2

z_c = 1.645

n = 11

iii. Compare your answers and explain their difference.

As the sample size increases and confidence level decreases the margin of error also decreases