Question

A certain type of thread is manufactured with a mean tensile strength of 79.3 kilograms and a standard deviation of 7.2 kilograms. How is the variance of the sample mean changed when the sample size is

(a) increased from 81 to 256?
(b) decreased from 324 to 64?

As in: The sample variance ____ from __ __ for n = 81 to ___ __ for n = 256

Answer 1

The variance of the sample mean decreases when the sample size is increased and increases when the sample size is decreased.

Step-by-step explanation:

When the sample size is increased from 81 to 256, the variance of the sample mean will decrease. The formula to calculate the variance of the sample mean is Variance of Sample Mean = (Population Variance) / Sample Size. So, as the sample size increases, the denominator in the formula increases and the variance of the sample mean decreases. To calculate the new variance, we can use the formula:

Variance of Sample Mean = (Population Variance) / Sample Size = (7.2^2) / 256 = 0.03 kilograms^2

When the sample size is decreased from 324 to 64, the variance of the sample mean will increase. Using the same formula, we can calculate the new variance:

Variance of Sample Mean = (Population Variance) / Sample Size = (7.2^2) / 64 = 0.81 kilograms^2