Question

a random sample size of 100 is selected from a population with P equals 40

Answer 1

SOLUTION:

From given data,

a random sample size of 100 is selected from a population with P equals 40

a) What is expected value of p(bar)?

b) What is standard error of p(bar)?

c) Show the sampling distribution of p(bar).

d) What does the sampling distribution of p(bar) show?

sample size = = 100

= 0.40

q = 1- = 1 -0.40 = 0.6

a) What is expected value of ?

( , ) , where

Mean = = = 0.4

E() =   = 0.4

The expected value of   is 0.40

b) What is standard error of ?

=

=

=  0.0489

The standard error of   is 0.0489

c) Show the sampling distribution of .

Sampling distribution can be approximated by normal if both p and q are 5 or more. Lets calculate,

p = 100*0.4 = 40 > 5

q = n*(1-p) = 100*(1-0.4)

= 100 *0.6

= 60 > 5

The conditions for normal approximation are satisfied

[ Note: Some professors say 15 or more , some say 10 or more and some say 5 or more . you need to fill the number with what you were taught

d) What does the sampling distribution of show

Taking normal approximation to binomial , the sampling distribution of sample proportion follows normal distribution.

Shape :(approximately)Normal

(0.4 , 0.0489²)

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