Question

2. Not only is the mean of pairs of clothes purchased is 10, but the population standard deviation is 4.5. When the researcher from problem number 1 calculates a standard deviation for the distribution of sample means for her 2,950, 000 samples, is the standard deviation of sample means likely to be less than, greater than, or equal to 4.5? Explain

Answer 1

Less than 4.5

Explanation:

Given that :

Mean = 10

Population standard deviation (σ) = 4.5

Sample size (n) = 2950000

The standard deviation of sample means becomes smaller or lesser as the sample size increases according to the central limit theorem. This is because the standard deviation of sample means is obtained by dividing the population standard deviation by the square root of the sample size. Thus is called the standard error.

The standard deviation of sample means is called the standard error ; and is obtained by:

Standard Error = σ/√n

Standard Error = 4.5 / √2950000

Standard Error = 4.5 / 1717.5564

= 0.0026200