Question

A simple random sample of 10 items resulted in a sample mean of 20. The population standard deviation is σ = 6. Round your answers to two decimal places.

a. What is the standard error of the mean, σ_x?

b. At 95% confidence, what is the margin of error?

Answer 1

Solution :

Given that,

= 62.5

= 6

n = 10

a ) The standard error of the mean, σ_x = (/ n)

= ( 6 10 )

= 1.90

The standard error of the mean, σ_x = 1.9

b ) At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z_/2* (/n)

= 1.960 * ( 6 10 )

= 3.72

Margin of error = E = 3.72