Question

how large of a sample is needed to estimate the mean of a normally distributed population for each of the following?a. ME= 5, sigma=40, alpha=0.01b. ME=10; sigma=40; alpha=0.01c. compare and comment on your answers to parts a and b.

Answer 1

Answer:

a: 425

b: 107

c: read below

Step-by-step explanation:

Assuming ME means Error:

We have:

n = to be determined

ME = 5

σ = 40

α = 0.01

The z-value we will use for α = 0.01 is: 2.575

See attached photo 1 for the calculation of n

For the second situation, it is calculated the same way, we just have E = 10

See second attached photo for the calculation of this value of n...

For part c:  The sample size is much smaller for the second situation because we are allowing more error in our estimate, so we can be less accurate.  We don't need as large of a sample size if we don't want to be as accurate