Question

Scores on the Gillian Autism Rating Scale (GARS) are normally distributed with a mean of 100 (µ =100) and a standard deviation of 15(σ=15). A sample of 64(n= 64) GARS scores is randomly selected and the sample mean is computed. a. Describe the distribution of such sample means? b. What is the mean of all such sample means? c. What is the standard deviation of all such sample means?

Answer 1

Answer:

The answer is below

Step-by-step explanation:

a) Given that the number of sample (n) = 64, therefore the since n > 30, the distribution of the sample means is going to be normally distributed.

b) The mean of the distribution of sample means (also known as the Expected value of M) is equal to the population mean μ.

$\mu_x$ = μ = 100

c) The standard deviation of the distribution of sample means is called the Standard Error of M, it is given by:

$\sigma_x=\frac{\sigma}{\sqrt{n} } =\frac{15}{\sqrt{64} } =1.875$