Question

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a) Suppose n = 43 and p = 0.26. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np = 11.18

nq = 31.82

What are the values of μ_p̂ and σ_p̂? (Use 3 decimal places.)

μ_p̂ =

σ_p̂ =

I know np and nq for sure but I am having a hard time determining μ_p̂ and σ_p̂

Answer 1

Solution :

(a)

We approximate by a normal distribution because np , nq > 10

The mean of the sampling distribution of proportion is ,

= p = 0.26

The standard deviation of the sampling distribution is ,  

=  [p( 1 - p ) / n = [(0.26 * 0.74) / 43] = 0.067