Question

Suppose a random sample of n measurements is selected from a binomial population with probability of success p = .39. Given n = 300, describe the shape, and find the mean and the standard deviation of the sampling distribution of the sample proportion, .

Answer 1

Answer:

The answer is below

Step-by-step explanation:

a) Given that the number of sample (n) = 300, therefore 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.

$\mu_x=\mu=np=300*0.39=117$

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

$\sigma_x=\sqrt{np(1-p)} =\sqrt{300*0.39(1-0.39)} =8.44$