Question

Consider a sampling distribution with p= 0.09 and samples of size n each. Using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion.a. For the random sample of size n= 4000b. For the random sample of size n= 1000c. For the random sample of size n= 500

Answer 1

Answer:

Step-by-step explanation:

Given that a a sampling distribution has  p= 0.09 and samples of size n each

Since proportion is for favour and other possible outcome is not favour we find that there are exactly two outcomes

Also each sample item is independent of the other

So X follows a binomial distribution with p = 0.09

We know that mean of a binomial distribution is

np

a) When n =4000, mean = $4000*0.09\\= 360$

b) when n =1000, mean = $1000*0.09 = 90$

c) when n =500, mean = $500*0.09 = 45$