Answer to Question #219138 in Statistics and Probability for Bebe

Question

Assuming that the samples come from normal distribution, find the margin of error E given the following:

n = 10 and x̄ = 28 with s = 4.0, 99 % confidence

n = 16 and x̄ = 50 with s = 4.2, 95 % confidence

Answer 1

1.

The value of z at 99% confidence level is 2.58.

The standard error is

$SE = \frac{s}{\sqrt{n}} \\ = \frac{4.0}{\sqrt{10}}=1.26$

The margin of error is

$ME = Z \times SE \\ = 2.58 \times 1.26= 3.26$

2.

The value of z at 95% confidence level is 1.96.

The standard error is

$SE = \frac{s}{\sqrt{n}} \\ = \frac{4.2}{\sqrt{16}}=1.05$

The margin of error is

$ME = Z \times SE \\ = 1.96 \times 1.05 = 2.058$